Question

What is the area of triangle ACB?

Answer 1

Hint: Here in this question, we will first do the required construction to prove that the triangle ACB is a right angled triangle. After this we will calculate the height and base of the triangle and finally use the formula to find the area of the triangle.

Complete step-by-step answer:
In this question we need to find the triangle ACB. We have drawn a line from the centre on the tangent.

We know that line drawn from centre to the tangent makes an angle of 90 degree with the tangent.
$\angle ORC = \angle OTC = {90^0}$.
Also we know that the length of tangent drawn from a point to a circle is of equal length.
So, the length of the tangent CT = CR =4 unit.
Therefore, ORCT is a square with each side length of 4unit.
$\therefore $ $\angle ACB$ is a right-angled triangle
Where AC = 8 unit and BC = CR + BR = 4+2 = 6 unit.
Now we know that
Area of a triangle = $\dfrac{1}{2} \times base \times height$.
Base of right triangle ACB = AC = 8 unit and height = BC =6 unit.
$\therefore $Area = $\dfrac{1}{2} \times 8 \times 4$= 16 sq. unit.
And hence the area of triangle ABC is 16 sq. unit.

So, the correct answer is “Option A”.

Note: In this type of question you should remember the theorem related to tangent of circle. This will help you to identify the type of triangle and also will be helpful in calculating sides in some other cases. You should know the formula for finding the area of a triangle.