Question

AB is a chord of a circle and AOC is its diameter such that angle ACB =50 degrees. If AT is the tangent to the circle at point A, then find angle BAT

Answer 1

Angle CBA =90°(angle in a semicircle is always 90°)

angle OAT =90°(tangent make 90°with radius)

angle(CBA+OAB+ACB)=180°(sum of angles of triangle)

90°+angle OAB+50°=180°
angle OAB=180-140
angle OAB=40

angle OAT=angle (OAB+BAT)

angle BAT=angle (OAT-OAB)
=90-40=50