Question

a chord 5cm apart from the centre of a circle is 24cm long .find the radius

Answer 1

Hi friend
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Your answer
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DISTANCE OF THE CHORD FROM CENTRE = 5 CM

LENGTH OF THE CHORD = 24 CM

THE PERPENDICULAR LINE ON THE CHORD FROM THE CENTRE MEASURING 5 cm WILL BISECT THE CHORD.

HALF LENGTH OF THE CHORD = 24/2 = 12 cm

NOW,

JOIN A LINE FROM THE CENTRE TO ONE END OF THE CHORD.

WE GET A RIGHT ANGLED TRIANGLE.
CONSIDER THE HYPOTENUSE AS THE RADIUS.

THEN,
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BY PYTHAGORAS THEOREM,
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$radius \: = \sqrt{(12) {}^{2} + (5) {}^{2} } \\ = \sqrt{144 + 25} \\ = \sqrt{169} \\ = 13 \: cm$
THEREFORE,
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RADIUS = 13 cm

HOPE IT HELPS

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