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.
In and ,
(Equal chords are equidistant from the centre)
( by construction)
Therefore, (By Right Angle Hypotenuse congruence condition)
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.).
Two concentric circles, with centre at O and common chord intersecting at A,B,C and D
Contruction, draw a line OM ⊥ AD, intersecting AD at M.
Now, since and is drawn from center O
Since O is also the center of inner circle, therefore OM also bisects BC as .
From (1) and (2),