1 answer:
1. Let O be the center of the sphere, A the tangency point and B the location of the satellite. (as in the figure below)
2. Join B to O. M(ABO)=

m(B)=(1/2)*138°=69°.
3. m(OAB)=90° as a radius to a tangency point is perpendicular to the tangent at that point.
4. m(AOB)=180°-90°-69°=21°.
5. check picture 2. Arc AM is equal to the measure of the central angle AOM = 21°.
6. The measure of the intercepted arc is 21°*2=42°
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