Question

1. Two circles whose centres are O and O' intersect at P. Through P, a line
parallel to 00', intersecting the circle at C and Dis drawn. Prove that
CD=200'.​

Answer 1

CD = 2OO'  

Step-by-step explanation:

Lets draw OA ⟂ CD and O'B  ⟂ CD

OA  ⟂ CD

⇒ CA = AP = 1/2 AP   ( as perpendicular from center bisect the chord)

⇒  CP = 2AP  

Similarly,  O'B  ⟂ CD

⇒ PB = BD = 1/2 PD

⇒ PD = 2PB

CD = CP + PD

= 2AP + 2PB = 2(AP + PB) = 2AB

AB = OO'  

CD = 2OO'  

QED

Proved

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Answer 2

Step-by-step explanation:

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