Question

In the given figure, AB is the diameter of the circle with centre O and AT is a tangent of the circle. Calculate the value of x.
[3 Marks]

Answer 1

∠ABC = $\frac{1}{2}$∠AOC
[Angle subtended at the center is double of the angle subtended at the other point on the circle] [1 Mark]

$\Rightarrow$ ∠ABC=$\frac{1}{2}$ X 80° = 40°
∠ BAT = 90° [Angle between the tangent and the diameter of the circle is 90°.] [1 Mark]

In △ BAT,
∠BAT+ ∠ABT+ ∠BTA =180°
[Sum angle property of the triangle]
$\Rightarrow$90°+40°+x=180°
$\Rightarrow$x=50° [1 Mark]