SOLUTION: Given: tangents AB and AC to ⊙O m∠ACB = 72° Find the following in degrees. mBC° mBDC° m∠ABC° m∠A°

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Question 1194108: Given: tangents AB and AC to ⊙O
m∠ACB = 72°
Find the following in degrees.
mBC°
mBDC°
m∠ABC°
m∠A°
Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

Two tangents to a circle from the same point are congruent. So triangle ABC is isosceles with base angles BCA and CBA and vertex angle A.

(1) Use that and the fact that the sum of the angles in a triangle is 180 degrees to find the measures of angle A and angle ABC.

(2) The two tangents cut the 360 degrees of the circle into two parts. If arc BC is x degrees, then the other arc is 360-x degrees.

Then the measure of angle A is half the difference between the measures of the two arcs:

Use that and the measure of angle A that you found in part (1) to find x, which is the degree measure of arc BC.

(3) It is impossible to find the measure of angle BDC, since point D is nowhere defined.