    Question

# In the given figure, lengths of the chords AB and CD are 12 cm and 18 cm respectively and distance between them is 15 cm. Find the radius of the circle. A

119 cm

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B

113 cm

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C

117 cm

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D

None of these

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Solution

## The correct option is D √117 cm Let the radius of the circle be r. Given, AB = 12 cm, CD = 18 cm and FE = 15 cm We know that perpendicular to the chord from the centre bisects the chord. ⇒AF=FB=AB2=6 cm and CE=ED=CD2=9 cm Let OE be x cm. Then OF=15−x cm. Applying Pythagoras theorem to △AFO, AO2=AF2+OF2 ⇒r2=62+(15−x)2 ... (i) Applying Pythagoras theorem to △CEO, OC2=CE2+OE2 ⇒r2=92+x2 ... (ii) Equating equations (i) and (ii), we get 62+(15−x)2=92+x2 ⇒36+(15−x)2=81+x2 ⇒36+225+x2−30x=81+x2 ⇒30x=180 ⇒x=18030=6 ⇒r2=92+62=117 ⇒ Radius, r =√117 cm.  Suggest Corrections  0      Similar questions  Related Videos   Circles and Their Chords - Theorem 3
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