In the figure above, the circle has center P and radius r. Lines AB and AC are tangent to the circle. If M is the midpoint of segment AC and the measure of angle PMC equals the measure of angle MPC, what is the length, in terms of r, of segment PA?
Choices:
A.r + 1
B.2*r
C.r*\sqrt{2}
D.r*\sqrt{3}
E.r*\sqrt{5}
Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.
Question: In the figure above, the circle has center P and radius r. Lines AB and AC are tangent to the circle. If M is the midpoint of segment AC and the measure of angle PMC equals the measure of angle MPC, what is the length, in terms of r, of segment PA?
Choices:
A.r + 1
B.2*r
C.r*\sqrt{2}
D.r*\sqrt{3}
E.r*\sqrt{5}
Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: In the figure above, the circle has center P and radius r. Lines AB and AC are tangent to the circle. If M is the midpoint of segment AC and the measure of angle PMC equals the measure of angle MPC, what is the length, in terms of r, of segment PA?
Choices:
A.r + 1
B.2*r
C.r*\sqrt{2}
D.r*\sqrt{3}
E.r*\sqrt{5}