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Question

In the above figure, CM is a tangent at point C. ABCD is a square. B is the centre of the circle. BM = 10 cm, CM = 8 cm. What is the value of AD?


A

6 cm

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B

4 cm

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C

9 cm

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D

8 cm

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Solution

The correct option is A

6 cm


Given, CM is a tangent at C and B is the centre of the circle.

BCM=90 [Tangent at any point of a circle and the radius through this point are perpendicular to each other]

Consider ΔBCM. It is a right angled Δ with right angle at C.

BC2+CM2=BM2 (Pythagoras theorem)
BC2+82=102BC2+64=100BC2=36
BC = 6

As ABCD is a square, BC = AD [All sides of a square are equal]

BC = AD = 6 cm


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