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Question

AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24cm. If the chords are on the opposite sides of the centre and the distance between them is 17 cm, then the radius of the circle is _____.

A
14 cm
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B
10 cm
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C
13 cm
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D
15 cm
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Solution

The correct option is C 13 cm

Given AB and CD are two chords of a circles on opposite sides of the centre.

Construction: Draw perpendiculars OE and OF onto AB and CD respectively from centre O.
AE = EB = 5cm and CF = FD = 12 cm
[ Perpendicular drawn to a chord from center bisects the chord]

Given,
Distance between two chords = 17 cm
Let distance between O and F =x cm
And distance between O and E =(17x) cm

In ΔOEB,
OB2=OE2+EB2
[Pythagoras theorem]
=(17x)2+52 ---(1)

In ΔOFD,
OD2=OF2+FD2
[Pythagoras theorem]
=(x)2+122----------→(2)

But OB = OD ( radii of the same circle).

From 1 & 2,
(17x)2+52=(x)2+122
289+x234x+25=x2+144
34x=170
x=5
Subsitute x in equation (2);
OD2=(5)2+122=169
OD=13
∴ Radius of the circle is 13 cm.

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