Question

In the given figure O, is the centre of the circle. CE is a tangent to the circle at A. If ∠ABD = 26° find:

1. ∠BDA
2. ∠BAD
3. ∠CAD
4. ∠ODB

Answer 1

Given ∠ABD = 26°

a. Angle in semi-circle is a right angle

∴ ∠BDA = 90°

b. Sum of all angles in a triangle = 180°

∴ ∠BAD + ∠BDA + ∠ABD = 180°

∠BAD + 90° + 26° = 180°

∠BAD = 180° – 116°

= 64°

c. Angles in alternate segments are equal

∴ ∠CAD = ∠ABD

= 26°

d. In ΔODB,

OB = OD   ...(Radii of same circle)

∴ ∠ODB = ∠OBD

= ∠ABD

= 26°