In the given figure, AB, AD and DC are the tangents at point B, E and C respectively. If BC = 5 cm, AB = 6 cm and the perimeter of the quadrilateral ABCD is 25 cm, then ED is equal to

6 cm

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4 cm

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8 cm

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10 cm

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Solution

The correct option is B
4 cm
Given: BC = 5 cm, AB = 6 cm and perimeter of ABCD = 25 cm

We know that, tangents drawn from an external point to a circle are equal in lengths.

$∴ A B = A E = 6 c m$
And, $E D = C D (s a y x) N o w, A B + B C + C D + E D + A E = 25 c m (G i v e n) \Rightarrow 6 + 5 + x + x + 6 = 25 c m \Rightarrow 17 + 2 x = 25 \Rightarrow 2 x = 25 - 17 \Rightarrow 2 x = 8 c m \Rightarrow x = \frac{8}{2} \Rightarrow x = 4 c m$

Thus, the value of ED is 4 cm.

Hence, the correct answer is option b .

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