In the given figure, CM is a tangent, ABCD is a square, and B is the centre of the circle. If BM = 10 cm and CM = 8 cm, what is the measure of AD?

6 cm

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4 cm

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9 cm

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8 cm

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Solution

The correct option is A 6 cm
In the given problem, CM $⊥$ BC.
(The tangent at any point of a circle is perpendicular to the radius through this point.)
Thus, $Δ$ BCM is right-angled at C.
Hence, by Pythagoras Theorem,
$B C^{2} = B M^{2} - C M^{2} = 36$
$\Rightarrow B C = 6 c m$

Given that ABCD is a square, AD = BC = 6 cm.

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Similar questions

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?

In a right-angled triangle, the length of the largest side is 10cm and of another side is 8cm. What will be the length of the remaining side?

△ A B C

c m^{2} .

A B C

A B = 10 cm

B C = 8 cm

A C = 6 cm

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