# NCERT Class 9 Solutions: Circles (Chapter 10) Exercise 10.5 – Part 4 (For CBSE, ICSE, IAS, NET, NRA 2022)

Get unlimited access to the best preparation resource for CBSE/Class-9 : get questions, notes, tests, video lectures and more- for all subjects of CBSE/Class-9.

Vertical opposite angles are the angles that are vertically opposite to each other when two lines intersect

Q-9 Two circles intersect at two points Q and B. Through Q, two line segments PQA and RQS are drawn to intersect the circles at P, A and R, and S respectively (see Fig.) . Prove that

Solution:

• Here, two circles intersect at two point Q and B.
• Two line segment PQA and RQS are drawn to intersect the circles at A, D and P, Q respectively
• Now, join PR and AS chords.

For chord PR,

• (Angles in the same segment) … equation (1)

For chord AS,

• (Angles in same segment) … equation (2)
• PQA and RQS are line segments intersecting at Q, therefore (Vertically opposite angles) … equation (3)

By the equations (1)

• ( From equation (3) )
• ( From equation (2) )

Q-10 If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.

Solution: