Question

AB is a chord of a circle with center O The tangent at B cuts AO produced at T if $\angle BAT={25}^{\circ }$ Then the value of $\angle BTA$ is

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${25}^{\circ }$
• D. ${40}^{\circ }$

Answer 1

The correct option is D ${40}^{\circ }$

The figure is shown in image

Draw the perpendicular from point $B$ to center $O$

From the property of the circle ,it is very clear that $\angle BOT$ is double of $\angle BAT$ .

Hence $\angle BOT={50}^o$

Now In $\Delta BOT$

$\angle TBO+\angle BOT+\angle BAT={180}^o$

Hence $\angle BTA=180-(50+90)$

$\angle BTA={40}^o$