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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=OQ2QL2
= 10282
=10064=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=OS2SM2
=10262
=10036
=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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