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Q.

AD and AE are the tangents to a circle with the center O. BC touches the circle at F and AE=5cm. The perimeter of ΔABC is ____ cm.

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Detailed Solution

AD and AE are the tangents to a circle with the center O. BC touches the circle at F and AE=5cm. The perimeter of ΔABC is 10cm.
We know that the tangents from an external point are equal.
The perimeter of a triangle is the sum of all sides.
Given is the following figure,
Question Image

Question Image

Since the tangents from an external point are equal,

∴ A D = A E, C D = C F, B E = B F

Perimeter of the triangle,

Δ A B C = A C + A B + C B

= A D − C D + C F + B F + A E − B F = A D − C F + C F + B F + A E − B F = A E + A E = 2 A E

We have,

A E = 5 cm

.
Perimeter of

Δ A B C

,

Therefore, the perimeter of

Δ A B C

is

10 cm

.

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