a. To prove that angle OAD = angle OBC, we can use the fact that tangents drawn to a circle from an external point are congruent.
Since OA and OB are tangents to circle O, we have:
OD = OD (common side)
OA = OB (tangents from external point)
Angle OAD = angle OBC (corresponding angles)
Therefore, by the SAS (side-angle-side) congruence rule, we have triangle OAD is congruent to triangle OBC.
b. Since triangle OAD is congruent to triangle OBC, we know that angle BOD = angle AOD = 64°.
Therefore, m BOD = 64°.
In circle O, and are
tangents. The figure is not
drawn to scale.
a. Prove that
.
b. Find m BOD for m
AOP = 64°. Explain
your reasoning.
(4 points)
1 answer
1 answer