Q7 of 31 Page 65

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.


Given, Concentric Circles, CD and AB chords.


To prove: AC = DB


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


In OAP and OBP, We have


AP = BP


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



In OCP and ODP


CP = DP



⇒ CA + AP = BP + DB


⇒ CA = DB + BP-AP


⇒ CA = DB + 0


⇒ CA = DB


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