Question

A straight line intersects one of the two concentric circles at the points A and B and
the other at the point C and D. I prove with reason that AC = DB.
7.​

Answer 1

Step-by-step explanation:

Given, Concentric Circles, CD and AB chords.

To prove: AC = DB

Construction: OP is a perpendicular bisector of CD and AB.

In traingle OAP and traingle OBP, We have

AP = BP

Perpendicular from the center of the circle to any Chord bisects it in two line segments

In traingle OCP and traingle ODP

CP = DP

⇒ CA + AP = BP + DB

⇒ CA = DB + BP-AP

⇒ CA = DB + 0

⇒ CA = DB