Question

In figure, a triangle is drawn to circumscribe a circle radius 10 cm such that the segment BD and DC into which BC is divided by point of contact D are of lengths 15 cm and 20 cm respectively. If area of triangle ABC=525cmsquare , then find the lengths of the sides AB and AC.

Answer 1

The formula I used is a shortcut method and can save a lots of time in exams

Answer 2

Concept introduction:

Circumscribe a circle means a triangle is drawn through a circle where a circle is inside the triangle.

Given:

Here it is given that radius is $10 cm$.

Area of triangle is $ABC=525cm^{2}$.

The segment $BD$ and $DC$ into which $BC$ is divided by point of contact $D$are of lengths $15cm$ and $20cm$ respectively.

To find:

We have to find the lengths of the sides $AB$ and $AC$.

Solution:

According to the question,

Perimeter of the triangle $ABC$ is

$=$$30+40+2x$

$=$$70+2x$

Semiperimeter $=35+x$

radius$=\frac{area}{semi perimeter}$

∴$10=\frac{925}{35+x}\\ x=17.5$

∴ $AB=(17.5+15)=32.5cm\\AC=(17.5+20)=37.5cm$

Hence the final answer is

$AB=32.5cm\\AC=37.5cm$.