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Question

# AB is chord of a circle with centre O and radius 17 cm. If OM⊥AB and OM=8 cm, then the length of chord AB is

A
12 cm
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B
30 cm
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C
15 cm
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D
24 cm
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Solution

## The correct option is A 30 cmGiven- O is the centre of a circle of radius 17 cm.OM⊥AB when AB is a chord of the given circle. To find out- the length of AB=? Solution-We join OA.So, OA is a radius of the given circle.∴OA=17 cm Now OM⊥AB⇒∠OMA=90oTherefore, ΔOMA is a right one with OA as hypotenuse.Therefore by Pythagoras theorem, we getAM=√OA2−AM2=√172−82cm =15cm . Again M is the mid point of AB, since OM⊥AB and we know that the perpendicular, from the centre of a circle to any of its chords, bisects the latter.∴AB=2AM=2×15 cm =30 cm

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