# NCERT Class 9 Solutions: Circles (Chapter 10) Exercise 10.4 – Part 2

Q-3 If two equal chords of a circle intersect within the circle; prove that the line joining the point of intersection to the centre makes equal angles with the chords.

Solution:

Given,

• AB and PQ are chords intersecting at S.

• , CD is the diameter.

To prove,

Now, Construction,

• Draw And OS is joined.

In and ,

• (Equal chords are equidistant from the centre)

• (Common line)

• ( by construction)

• Therefore, (By Right Angle Hypotenuse congruence condition)

Therefore,

• by Corresponding Parts of Congruent Triangles

• (Same angle)

Q-4 If a line intersects two concentric circles (circles with the same centre) with centre O. A common chord intersects the circles at A, B, C and D, prove that AB = CD (see Fig.).

Solution:

Given,

Two concentric circles, with centre at O and common chord intersecting at A,B,C and D

Now, since and is drawn from center O

• OM is bisects of AD as .

• …………equation (1)

Since O is also the center of inner circle, therefore OM also bisects BC as .

• Therefore, …….equation (2)

From (1) and (2),

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