Question

In the given figure, a circle is inscribed in a right-angled triangle such that $AF=6\text{cm}$ and $EC=15\text{cm}$. The perimeter of the triangle is:

• A. $68\text{cm}$
• B. $70\text{cm}$
• C. $72\text{cm}$
• D. $74\text{cm}$

Answer 1

The correct option is B $70\text{cm}$

In the given problem, $AF=AE=6\text{cm}$
$CE=CD=15\text{cm}$
Let $BF=BD=x\text{cm}$ } (The two tangents from an external point to a circle are equal in length)

Thus, by Pythagoras theorem,
$(6+x{)}^2+(6+15{)}^2=(15+x{)}^2$
$\Rightarrow 18x=252$
$\Rightarrow x=14$

Hence, perimeter $=(6+15+15+14+14+6)=70\text{cm}$