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Question

In the figure given, O is the centre of the circle. AB and CD are two chords of the circle. OM is perpendicular to CD and ON is perpendicular to AB. AB=24 cm,ON=5 cm,OM=12 cm. Find the length of chord CD
584887_0e883d8d1f554ab6a0f01ada770592f8.png

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Solution

Given: AB=24 cm;ON=5 cm,OM=12 cm.
ONAB
N is the mid point of AB.
AN=242cm=12 cm.
Now from ANO,
AO2=ON2+AN2
r2=52+122 (AO=CO=r)
r2=25+144
r=13

So,AO=CO=13 cm

From ΔCMO,
CM2=CO2OM2
CM2=132122
CM2=169144
CM2=25
CM=5
As OMCD,M is the mid point of CD.
CD=2 CM=2×5 cm=10 cm.

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