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Question

# In the given figure, O is the centre of the circle. AB and CD are two chords of the circle. OM is perpendicular to AB and ON is perpendicular to CD. AB=24 cm,OM=5 cm,ON=12 cm. Find the:(i) radius of the circle.(ii) length of chord CD.

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Solution

## This question is solely based on the property that perpendicular dropped from the centre of the circle on any chord of that circle will bisect the chord.Solving (i)⇒AM=BM=AB2=12cmNow by applying Pythagorous theorem in △OMB⇒OB2=OM2+MB2⇒R2=52+122=25+144=169[∵OB=Radius] ⇒R=13Solving (ii)Applying Pythagorous theorem in △OCN⇒OC2=ON2+NC2[∵OC=Radius=13]⇒132=122+NC2⇒NC2=169−144=25⇒NC=5Now,since ON is perpendicular to the chord CD⇒ N is mid point of chord CD⇒CD=2×NC=2×5=10Hence, answer of (i) is 13 and that of (ii) is 10

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