Question

△ABC is inscribed in a circle. Find the angle between the tangents to the circle at points B and C, if m∠CAB=50°.

Answer 1

Answer:

80°

Step-by-step explanation:

We know the measure of ∠CAB.  This is an inscribed angle; this means its measure is 1/2 that of the intercepted arc, BC.  This means the measure of BC is 100°.

This makes the measure of arc BAC is 360-100 = 260°.

The measure of the angle formed by the tangents, since it is outside the circle, will be 1/2 of the difference of the intercepted arcs.  This means the measure of this angle will be

1/2(260-100) = 1/2(160) = 80°

Answer 2

Based on the information given, it should be noted that the angle between the tangents to the circle at points B and C will be 80°.

• From the given information, we've been given the measure of ∠CAB which is 50°.

• Since this is an inscribed angle, it implies that the measure is 1/2 that of the intercepted arc, BC. Therefore, the measure of BC will be: = 50/0.5 = 100°.

• Therefore, the measure of arc BAC will be: = 360° - 100° = 260°.

It should be noted that the angle between the tangents to the circle at points B and C will therefore be calculated thus:

= 1/2(260-100)

= 1/2(160)

= 80°

In conclusion, the correct option is 80°.

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