Answer:
a. ∡AOP = ∡BOP bounded by AO = BO and common segment OP
b. ∡BOD is 116°
Step-by-step explanation:
Here, we have;
Line AO = BO → Radius of circle
∡OAP = ∡OBP = 90° →Tangent angle to a circle
Therefore, AP = BP = √((OP)² - (BO)²) = √((OP)² - (AO)²)
Hence since AO = BO and AP = BP as well as ∡OBP = ∡OAP, which are two sides and an included angle to completely define a triangle, we have that triangles APO is congruent to triangle BPO.
b. Here we have ∡AOP = 64°
Where, triangles APO and BPO are congruent, therefore ∡AOP = ∡BOP since the adjacent sides to the angles, AO and OP are equal to BO and OP
∴ ∡BOP = ∡AOP = 64°
Angle ∡BOD + ∡BOP = 180° = sum of angles on a straight line
Therefore, ∡BOD + 64° = 180° and ∡BOD = 180 - 64 = 116°
∡BOD = 116°.
