In figure, O is the centre of the circle, CA is tangent at A and CB is tangent at B drawn to the circle. If ∠ACB=75o, ∠AOB=
Given- O is the
centre of a circle to which two tangents, CA&CB have been drawn at A&B respectively. ∠ACB=75o.
To find out- ∠AOB=? Solution- OA&OB are radii drawn from O to A&B respectively.
∴∠OBC=90o=∠OAC since the radius through the
point of contact of a tangent to a circle is perpendicular to the tangent. Now, considering the
quadrilateral AOBC, we have ∠OBC+∠OAC+∠ACB+∠AOB=360o (by angle sum property of quadrilateral)
⟹90o+90o+75o+∠AOB=360o⟹∠AOB=105o.
Ans- Option D.