Question

A circle is inscribed in a right triangle ABC, right angled at C. The circle is tangent to the segment AB at D and length of segments AD and DB are 7 and 13 respectively. Area of triangle ABC is equal to

• A. 91
• B. 96
• C. 100
• D. 104

Answer 1

The correct option is A 91

C = 20
$2s=a+b+c$
$2s=r+13+20+7+r$
$s=\frac{40+2r}{2}\Rightarrow 20+r$
$(r+13{)}^2+(r+2{)}^2=20$
S – a = 7
S – b = 13
a – b = 6 ……(1)
$a^2+b^2=400$
$(a-b{)}^2+2ab=400$
$\Rightarrow ab=182$
$\Delta =\frac{1}{2}ab=91$