In the figure, and are tangents to the circle from point D . If m = 84 ° , find m .
A)42 °
B)84 °
C)96 °
D)None of These

Question

In the figure,  and  are tangents to the circle from point D . If m  = 84 ° , find m  .
A)42 ° 
B)84 ° 
C)96 ° 
D)None of These

Quizplus · Accepted Answer

Since the two tangent lines are drawn from the same point D, they are equal in length. Therefore, the angles opposite those tangent lines (11ebfb55_24ad_21c4_9d86_27d2206dcd6d_TBX8811_11 and the unknown angle) are also equal in measure. Thus, m 11ebfb55_24ad_21c5_9d86_9fc040867449_TBX8811_11 = m 11ebfb55_24ad_21c4_9d86_27d2206dcd6d_TBX8811_11 = 84 ° + 12 ° = 96 ° (since the angle between a tangent and a chord is half the measure of the intercepted arc). Therefore, the answer is (C) 96 °.

In the Figure, and Are Tangents to the Circle