Mathematics
In the figure (ii) given below, P is a point of intersection of two circles with centers C and D. If the st. line APB is parallel to CD, prove that AB = 2CD.
Circles
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Answer
From C, D draw CM, DN perpendiculars to AB.
From figure,
MCDN is a rectangle.
∴ MN = CD (Opposite sides of rectangle are equal).
Since, the perpendicular to a chord from the centre of the circle bisects the chord,
∴ MP = AP and NP = PB
From figure,
MN = MP + PN
= AP + PB
= (AP + PB)
= AB
∴ CD = AB [∵ MN = CD]
⇒ AB = 2CD
Hence, proved that AB = 2CD.
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