A triangle ABC is drawn to circumscribe a circle such that the segments BS and SC are of lengths 6 cm and 8 cm respectively. If the length of the segment AT is x cm , then find the perimeter of the triangle.

12+x

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24+2x

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28+2x

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14+x

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Solution

The correct option is C
28+2x

The tangents drawn from an external point to the circle are equal in length.

So,
AR = AT = x
[AR and AT are two tangents drawn from an external point A]

BR = BS = 6
[BR and BS are two tangents drawn from an external point B]

CT = CS = 8
[CT and CS are two tangents drawn from an external point C]

So, AB = AR + BR = 6 + x

BC = BS + SC = 14

AC = AT + TC = 8 + x

Therefore, perimeter of the triangle
= Sum of all sides
= (6 + x) + (14) + (8 + x)
= 28 + 2x

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