Question

PLEASE HELP 100 POINT REWARD.SHOW WORK AND EXPLAIN

Given: The circles share the same center, O, BP is tangent to the inner circle at N, PA is tangent to the inner circle at M, mMON = 120, and mAX=mBY = 106.

Find mP. Show your work.

Find a and b. Explain your reasoning

Answer 1

Check the picture below.

since the points of tangency at N and M are right-angles, and NY = MX, then we can run an angle bisector from all the way to the center, giving us P = 30° + 30° = 60°.

now for the picture at the bottom, we have the central angles in red and green yielding 106°, running an angle bisector both ways one will hit N and the other will hit M, half of 106 is 53, so 53°, so subtracting from the overlapping central angle of 120°, 53° and 53°, we're left with b = 14°.

Now, the central angle of 120° is the same for the inner circle as well as the outer circle, so "a" takes the slack of 360° - 120° = 240°.