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Question

# PQ and RS are two parallel chords of a circle whose centre is O and radius is 10 cm. If PQ=16 cm and RS=12 cm. Find the distance between PQ and RS if they lie on the opposite side of the centre.

A

14 cm

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B

12 cm

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C

10 cm

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D

11 cm

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Solution

## The correct option is B (14 cm) Given PQ=16 cm ⇒PL = LQ =162= 8cm as the perpendicular from the centre of the circle bisects the chord. △OQL is a right angled triangle.From Pythagorean theorem, we have OQ2=OL2+LQ2 ⇒ OL2=OQ2−QL2 = 102−82=100−64=36∴ OL=√36 = 6 cm And also, RS=12 cm ⇒RM = MS = 6cm [the perpendicular from the centre of the circle bisects the chord.] Similarly, △OSM is a right angled triangle.Using Pythagoras theorem, OS2=OM2+SM2⇒OM2=OS2−SM2=102−62=100−36=64⇒OM=√64∴OM=8 cm ∴ LM=LO+OM=8+6=14 cm Hence, the distance between the two chords is 14 cm.

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