Question

In the given figure, ABC is a triangle, AB and AC are tangents, $\angle BAC={90}^{\circ },$ radius of the two circles are $8cmand10cm.$ The area of the $\Delta ABC$

• A.
  $180c{m}^2$
• B.
  $200c{m}^2$
• C.
  $150c{m}^2$
• D.
  $160c{m}^2$

Answer 1

The correct option is D

$160c{m}^2$
Given: $\angle BAC={90}^{\circ }$

Now, AB is a tangent to the second circle.

This implies that AC is the diameter of the second circle.

Also, AC is a tangent to the first circle.

This implies that AB is the diameter of the first circle.



$AB=2\times 8=16cm(\because EA=8cm)AC=2\times 10=20cm(\because AF=10cm)\therefore Areaof\Delta ABC=\frac{1}{2}\times AB\times AC(\because \text{ABC is a right angle triangle})=\frac{1}{2}\times 16\times 20=16\times 10=160c{m}^2$

Hence, the correct answer is option (d).