Question

In the given figure 3, AB is a chord of circle and AOC is diameter such that angle $ACB={55}^{\circ }.$ If AT is a tangent to the circle at point A, then angle BAT is :

• A. ${65}^{\circ }$
• B. ${40}^{\circ }$
• C. ${50}^{\circ }$
• D. ${55}^{\circ }$

Answer 1

Answer: (D)

${55}^{\circ }$

AT is tangent to a circle

$\angle BCA=55$

$\angle ABC={90}^{\circ }$ (diameter subtends a right angle at any point on circumference)

In triangle ABC, $\angle BAC+\angle ABC+\angle BCA={180}^{\circ }$

Thus, $\angle BAC+{90}^{\circ }+{55}^{\circ }={180}^{\circ }$

Thus, $\angle BAC={35}^{\circ }$

$\angle BAT+\angle BAC={90}^{\circ }$
So, $\angle BAT+{35}^{\circ }={90}^{\circ }$

Therefore $\angle BAT=55$

option D will be the answer