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Construction

To draw a pair of tangents to a circle which are inclined to each other at an angle of 60°, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be

(A) 135° (B) 90° (C) 60° (D) 120°

Construction

To  construct  a  triangle  similar  to  a  given  ∆ABC  with  its  sides 8/5 of  the  corresponding sides of ∆ABC draw a ray BX such that ∠CBX is an acute angle and X is on the opposite side of A with respect to BC. The minimum number of points to be located at equal distances on ray BX is

(A) 5 (B) 8 (C) 13 (D) 3

Construction

To  construct  a  triangle  similar  to  a  given  ∆ABC  with  its  sides 3/7  of  the corresponding sides of ∆ABC, first draw a ray BX such that ∠CBX is an acute angle and X lies on the opposite side of A with respect to BC. Then locate points B₁, B₂, B₃, … on BX at equal distances and next step is to join

(A) B₁₀ to C (B) B₃ to C  (C) B₇ to C (D) B₄ to C

Construction

To divide a line segment  AB in the ratio 5 : 6, draw a ray AX such that ∠BAXis  an  acute  angle,  then  draw  a  ray  BY  parallel to AX  and  the  points A₁, A₂, A₃,  …  and  B₁,  B₂,  B₃,  …  are  located  at  equal  distances  on  ray AX and BY, respectively. Then the points joined are

(A) A₅ and B₆ (B) A₆ and B₅ (C) A₄ and B₅ (D) A₅ and B₄

Construction

To divide a line segment AB in the ratio 4:7, a ray AX is drawn first such that∠BAX is an acute angle and then points A₁, A₂, A₃, …. are located at equal distances on the ray AX and the point B is joined to

(A) A₁₂ (B) A₁₁ (C) A₁₀ (D) A₉

Construction

To divide a line segment AB in the ratio 5:7, first a ray AX is drawn so that ∠BAX is an acute angle and then at  equal distances points are marked on the ray AX such that the minimum number of these points is

(A) 8 (B) 10 (C) 11 (D) 12 

Construction

To draw a pair of tangents to a circle which are inclined to each other at an angle of 35°, it is required to draw tangents at the end points of those two radii of the circle, the angle between which is

(A) 105° (B) 70° (C) 140° (D) 145°

Construction

To divide a line segment AB in the ratio p : q (p, q are positive integers), draw a ray AX so that ∠BAX is an acute angle and then mark points on ray AX at equal distances such that the minimum number of these points is

(A) greater of p and q (B) p + q (C) p + q – 1 (D) pq Solution : Answer (B)

Circles

A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. AP  and AQ  are  the  tangents  to  the  circle  at  P  and  Q.  If  a  tangent  BC  is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, find the perimeter of the ∆ABC.

Circles

 If an isosceles triangle ABC, in which AB = AC = 6 cm, is inscribed in a circle of radius 9 cm, find the area of the triangle.