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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.

Circles

The tangent at a point C of a circle and a diameter AB when extended intersect at P. If  ∠PCA =110º , find  ∠CBA

Circles

In Figure. O is the centre of a circle of radius 5 cm, T is a point such that OT = 13 cm and OT intersects the circle at E. If AB is the tangent to the circle at E, find the length of AB.

Circles

In Figure, the common tangent, AB and CD to two circles with centres O and O’ intersect at E. Prove that the points O, E, O’ are collinear.