In the given figure, a circle touches all the four sides of a quadrilateral ABCD whose three sides are AB = 6 cm, BC =7 cm, CD = 4 cm, then AD equals _____.

10 cm

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13 cm

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11 cm

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3 cm

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Solution

The correct option is D 3 cm
We know that from a point outside the circle, the two tangents to the circle are equal.
$=> A P = A S P B = B Q C R = C Q D R = D S$
Adding all we get,
$A P + P B + C R + D R = A S + B Q + C Q + D S => A B + C D = A D + B C => 6 + 4 = A D + 7$
$∴ A D = 3$ units

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Similar questions

In the given figure, a circle touches all the four sides of a quadrilateral ABCD whose three sides are AB = 6 cm, BC = 7 cm and CD = 4 cm. Find AD.

A B = 6 c m, B C = 7 c m

C D = 4 c m

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