Constructions (Q.1) In a figure, line segment of 8cm divides internally in the ratio 3:4. Which of the following (1 Mark) figure is correct?
(A) (i)(B) (ii)(C) (iii)(D) Both (i) and (iii) (Q.2) In the figure, AP=6cm, CD=2.8cm and DP=4.2cm. Measure the length of BP.
(1 Mark)
(A) 6.8cm(B) 5.8cm(C) 4.9cm(D) 2.9 cm (Q.3) In a figure, find angle C'.
(1 Mark)
(A) 600(B) 45°(C) 30°(D) 150 (Q.4) A line segment AB of length 8.0 cm, A4C||A7B divides it in the ratio 4:3 internally, why?
(A) By Pythagoras theorem(B) By Mid -Point Theorem(C) By Basic Proportionality Theorem (D) By Euclids Postulate (Q.5) In figure, AD is the bisector of angle A. If BD=4cm, DC=3cm and AB=6cm, find the measurement of AC.
(A) 4.5cm(B) 4cm(C) 3.5cm(D) 3cm (Q.6) In figure, find , where O is the center and PT is tangent on the circle at point P.
(A) 45°(B) 60°(C) 90°(D) 75° (Q.7) In a figure, measurement of a segment AQ=7cm, OQ=3cm. What will be the measurement of AP?
(1 Mark)
(1 Mark)
(1 Mark)
(1 Mark)
(A) 3cm(B) 7 cm(C) 10 cm(D) 12 cm (Q.8) The angle between tangent at a point on a circle and the radius through the point is(A) 45°(B) 60°(C) 90°(D) 1200 (Q.9) A tangent to a circle of radius 4cm from a point on the concentric circle of radius 6cm and measure its length.
(1 Mark) (1 Mark)
(A) 2.5cm(B) 3.7cm(C) 4.47cm(D) 5.6cm (Q.10) When a line segment of 6cm is divided into 2:3 internally, which figure is correct?
(1 Mark)
(A) (i) (B) (ii)(C) (iii)(D) Both (ii) and (iii) (Q.11) In the figure, find the ratio of triangle AB'C'.
(1 Mark)
(A) 1/2(B) 3/2(C) 2/3(D) 1/3 (Q.12) In a figure, PA and PB are tangents to the circle drawn from an external point P. CD is a third tangent touching the circle at Q. If PB=10cm and CQ=2cm, what is the length of PC?
(A) 20cm(B) 10cm(C) 8cm(D) 5 cm (Q.13) The common point of a tangent and circle is called(A) Point of contact(B) Secant(C) Center(D) Intersection of line (Q.14) O is the center of a circle of radius 8cm. The tangent at a point A on the circle cuts a line through O at B such that AB=15cm. Find the measurement of OB.
(1 Mark)
(1 Mark) (1 Mark)
(A) 18(B) 17(C) 16(D) 15 (Q.15) Measure the distance between two parallel tangents of a circle whose radius is 3cm.
(1 Mark)
(A) 3cm(B) 6cm(C) 9cm(D) 12cm (Q.16) Two tangents TP and TQ are drawn to a circle with center O from an external point T.
(1 Mark)
Which of the following is correct? (A) angle PTQ = 2 angle OPQ(B) angle PTQ = angle OPQ(C) 2 angle PTQ = angle OPQ(D) angle PTQ = angle TQP (Q.17) The tangents drawn at the ends of a diameter of a circle are parallel. Find angle 1 and angle 2.
(1 Mark)
(A) 45°, 45°(B) 90°, 90°(C) 45°, 90°(D) 300 ,600 (Q.18) In given figure, which of the following is correct?
(1 Mark)
(A) Triangle AB1C1 = (Triangle ABC)(B) Triangle AB1C1 = 1/3(Triangle ABC) (C) Triangle AB1C1 = 2/3(Triangle ABC)(D) TriangleAB1C1 ABC (Q.19) A point P is 13cm from the center of the circle. The length of the tangent drawn from P to the circle is 12cm. Measure the radius of the circle.
(1 Mark)
(A) 12cm(B) 10cm(C) 6cm(D) 5cm (Q.20) A circle is of diameter 12cm. From a point P, 10cm away from its center, constructing a pair of tangents to the circle. Measure the length of tangent segment.
(1 Mark)
(A) PA = PB = 5cm(B) PA = PB = 6cm(C) PA = PB = 8cm(D) PA=PB=9cm (Q.21) In figure, find the ratio.
(A) 1:5(B) 2:5(C) 2:3(D) 1: 3 (Q.22) In figure, two circles with centers A and B and of radii 5cm and 3cm touch each other internally. If the perpendicular bisector of segment AB meets the bigger circle in P and Q. Measure the length of PQ.
(A) 4.56cm(B) 5.41 cm(C) 7.32cm(D) 9.00 cm (Q.23) In figure, two circles with centers A and B and of radii 7cm and 3cm touch each other internally. If the perpendicular bisector of segment AB meets the bigger circle in P and Q. Measure the length of PQ.
(1 Mark)
(1 Mark)
(1 Mark)
(A) 7.32cm(B) 6.69cm(C) 5.41cm(D) 4.41 cm (Q.24) A point P is 10cm from the center of the circle. The length of the tangent drawn from P to the circle is 6cm. Measure the radius of the circle.
(1 Mark)
(A) 10cm(B) 8cm(C) 4cm(D) 3 cm (Q.25) In given figures, a line segment AB of length 10.0cm is divided by another line internally, in the ratio 3:2. Which figure is correct?
(1 Mark)
(A) (i)(B) (ii)(C) (iii)(D) Both (i)and (iii) (Q.26) A tangent to a circle of radius 6cm from a point on the concentric circle of radius 8cm and measure its length.
(A) 2.5cm(B) 5.28cm(C) 6.47cm(D) 7.6cm (Q.27) In a figure, find angle C.
(1 Mark)
(1 Mark)
(A) 105°(B) 65°(C) 45°(D) 300 (Q.28) In a triangle ABC from the vertices A , perpendicular drawn to the base bisects the base the triangle is . (A) Isosceles(B) right angled (C) equilateral triangle(D) scalene
(1 Mark)
(Q.29) Draw a line AB = 12 cm and divide it in the ratio = 3:5, measure the two parts.
(3 Marks)
(Q.30) Draw a circle of radius 3 cm, from a point 5 cm away from the centre of the circle, draw two tangents to the circle. Find the length of the tangents.
(3 Marks)
[CBSE-DELHI 2007]
[CBSE-Outside Delhi 2007]
(Q.31) Draw a circle of radius 6 cm. At a point A on it . Draw a tangent to the circle using the (3 Marks) [CBSE-Outside center. Delhi 2007] (Q.32) Construct a triangle similar to a given triangle ABC such that each of its sides is (4 Marks) 2/3rd of the corresponding side of the triangle ABC. It is given that AB = 4 cm , BC = [CBSE-DELHI 2006] 5 cm and AC = 6 cm . Also write the step of construction.
(Q.33) Construct a triangle ABC in which BC = 7 cm,
and median AD = 5 cm. Write the steps of
construction also.
(Q.34) Draw a circle of radius 3.5 cm. From a point P outside the circle at a distance of 6 cm from the center of circle, draw two tangents to the circle. (Q.35) Construct a quadrilateral ABCD with AB = 3 cm, AD = 2.7 cm, BD = 3.6 cm, ZB= 120° and BC = 4.2 cm. Construct another quadrilateral A'BC'D' similar to quadrilateral ABCD so that diagonal BD' & 4.8 cm (Q.36) Construct a triangle ABC in which BC =6 cm, Also, construct another triangle BPQ similar to Also write the steps of construction.
and median AD =5 cm. such that the side
(4 Marks) [CBSE-Outside Delhi 2006]
(4 Marks) ] (4 Marks)
[CBSE-DELHI 2005
[CBSE-Outside
] (4 Marks) [CBSE-DELHI 2003] Delhi 2005
.
(Q.37) Construct a in which AB = 6.5 cm, and BC = 5.5 cm. Also construct a similar to , whose each side is 3/2 times the corresponding side of the . (Q.38) Draw a ABC with side BC= 6 cm and AB = 5 cm and ABC = 60 . Construct a
(3 Marks) ] (3 Marks) ]
[CBSE-DELHI 2008
[CBSE-Outside Delhi 2008
AB’C’ whose sides are of the corresponding sides of ABC. (Q.39) Draw a line segment of length 8.1 cm and divide it in the ratio 4:5. Measure the two parts. (Q.40) Construct an isosceles triangle whose base is 8 cm and altitude 4 cm. Then construct another triangle
(5 Marks) (5 Marks)
whose sides are
times the corresponding sides of the isosceles triangle.
(Q.41) Draw a triangle ABC with sides BC = 7 cm, B = 45 , A = 105 . Then construct a triangle whose sides are 4/3 times the corresponding sides of ABC.
(5 Marks)
(Q.42) Draw a right triangle in which the sides (other than hypotenuse) are of length 4 cm and (5 Marks) 3 cm. Then construct another triangle whose sides are 5/3 times the corresponding sides of the given triangle. (Q.43) Draw a circle of radius 8 cm. From a point 12 cm away from its centre, construct the pair of tangents to (5 Marks) the circle and measure their lengths.
(Q.44) Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an (5 Marks) angle of 60 . (3 Marks) (Q.45) Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle. (Q.46) Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle.
(3 Marks)
Most Important Questions (Q.1) Draw a pair of tangents from a point 7 cm away from the centre of the circle whose radius is 3 cm. (Q.2) Draw a pair of tangents from a point 6 cm away from the centre of the circle whose radius is 4 cm. (Q.3) Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 120°. (Q.4) Draw a pair of tangents to a circle of radius 7 cm which are inclined to each other at an angle of 60°. Justify the construction. (Q.5) Construct a right triangle ABC right angled at B with sides 6 cm and 8 cm. BD is perpendicular from B on AC. Construct a circle through B, C and D and tangents from A to this circle. (Q.6) Construct a tangent to a circle of radius 3 cm from a point on the concentric circle of radius 5 cm. (Q.7) Draw a line segment 7 cm. Taking P as centre, draw a circle of radius 4 cm. and taking Q as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle. (Q.8) Draw a line segment 8 cm. Taking P as centre, draw a circle of radius 4 cm. and taking Q as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle. (Q.9) Draw a line segment AB of length 8.8cm and divide into two segments AP and PB such that point P divides the line segment AB in the ratio of AP : PB = 5 : 4. (Q.10) Draw a line segment AB of length 7.3 cm and divide into two segments AP and PB such that point P divides the line segment AB in the ratio of AP : PB = 2 : 5. (Q.11) Draw a line segment of length 6.2 cm and divide it in the ratio 5 : 3. Justify the construction.
(Q.12) (Q.13)
(Q.14)
(Q.15) Construct a right angled triangle with sides 3 cm and 4 cm. construct another triangle similar to it whose sides are 3/2 times the corresponding sides of first triangle.
(Q.16)
Mathematics for Class X Constructions -01 Q.1) Draw a line segment of length 8.1 cm and divide it in the ratio 4:5. Measure the two parts. (5 Marks) Q.2) Construct an isosceles triangle whose base is 8 cm and altitude 4 cm. Then construct another triangle whose sides are (5 Marks) Q.3) Draw a triangle ABC with sides BC = 7 cm, B = 45 , A = 105 . Then construct a triangle whose sides are 4/3 times the corresponding sides of ABC. (5 Marks) Q.4) Draw a right triangle in which the sides (other than hypotenuse) are of length 4 cm and 3 cm. Then construct another triangle whose sides are 5/3 times the corresponding sides of the given triangle. (5 Marks) times the corresponding sides of the isosceles triangle.
