All the sides of the triangle ABC are tangential to the circle with centre R. What is the perimeter of $Δ A B C$ ?

28 cm

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20 cm

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5 cm

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30 cm

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Solution

The correct option is A
28 cm

If two tangents are drawn to a circle from an exterior point, then the tangents are equal in length.

In the above figure,
AX = AZ = 3 cm (Tangents from an exterior point are equal in length)
Similarly, XB = BY = 7 cm
And, YC = ZC = 4 cm

$∴$ Perimeter of $Δ A B C$ = AB + BC + CA

= 10 + 11 + 7

= 28 cm

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Similar questions

All the sides of the quadrilateral ABCD are tangential to the circle with centre M. What is the perimeter of the quadrilateral ABCD?

An isosceles trapezium has an area of $36 c m^{2}$ , the parallel sides are $12 c m$ and $6 c m$ respectively. The perimeter of the trapezium is

\frac{r}{2} \times p e r i m e t e r o f t r i a n g l e A B C

O

△ A B C

B C, C A

A B

D, E

F

A F =

△ A B C - B C

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