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AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24 cm. If the chords are of the opposite sides of the centre and distance between them is 17 cm, then the radius of the circle is
Correct Answer:
Description for Correct answer:
Let radius of the circle be r.
Given, MN = 17 cm
Let ON = x
Then, OM = 17 - x
\( \Large \triangle AOM, \)
\( \Large OA^{2} = OM^{2} + AM^{2} \)
=> \( \Large r^{2} = \left(17-x\right)^{2} + 5^{2} \)
= \( \Large 289 + x^{2} - 34x + 25 \)
\( \Large r^{2} = 314 + x^{2} - 34x \) ...(i)
\( \Large OC^{2} = ON^{2} + CN^{2} \)
=> \( \Large r^{2} = x^{2} + 12^{2} = x^{2} + 144 \) ...(ii)
From Eqs. (i) and (ii), we get
\( \Large 314 + x^{2} - 34x = x^{2} + 144 \)
=> 34x = 170
=> x = 5
From Eq. (ii), \( \Large r^{2} = 25 + 144 = 169 \)
r = 13 cm
Let radius of the circle be r.
Given, MN = 17 cm
Let ON = x
Then, OM = 17 - x
\( \Large \triangle AOM, \)
\( \Large OA^{2} = OM^{2} + AM^{2} \)
=> \( \Large r^{2} = \left(17-x\right)^{2} + 5^{2} \)
= \( \Large 289 + x^{2} - 34x + 25 \)
\( \Large r^{2} = 314 + x^{2} - 34x \) ...(i)
\( \Large OC^{2} = ON^{2} + CN^{2} \)
=> \( \Large r^{2} = x^{2} + 12^{2} = x^{2} + 144 \) ...(ii)
From Eqs. (i) and (ii), we get
\( \Large 314 + x^{2} - 34x = x^{2} + 144 \)
=> 34x = 170
=> x = 5
From Eq. (ii), \( \Large r^{2} = 25 + 144 = 169 \)
r = 13 cm
Part of solved Geometry questions and answers : >> Elementary Mathematics >> Geometry
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