Thus, Both the triangle ΔAPO ≅ ΔBPO and angle ∠BOD is 116°.
What is a circle?
The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r²,
where h, k is the coordinate of the circle's center on a coordinate plane and r is the circle's radius.
Part A.
Since Point p is outside the circle, PA and PB are tangent to the circle.
There is a property of a circle that the length of the tangent drawn from a single point to the circle is equal in length. So,
PA = PB
∠A = ∠B (angle between tangent and radius is always 90°)
AO = BO (they are the radius of the circle)
APO ≅ BPO
Hence both the triangle APO and BPO are congruent by SAS.
Therefore,
∠AOP = ∠POB = 64°(given)
Part B.
∠BOD = ?
∠BOD + ∠POB = 180
∠BOD + 64 = 180
∠BOD = 180 - 64
∠BOD = 116
Thus, Both the triangle ΔAPO ≅ ΔBPO and angle ∠BOD is 116°.
Learn more about circle here:
brainly.com/question/11833983
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