Problem: In circle O, the midpoint of radius OX is Q; at Q, AB⊥XY. The semi-circle on AB as diameter intersects XY in M. Line AM intersects circle O in C, and line BM intersects circle O in D. Line AD is drawn. Then, if the radius of circle O is r,AD is:
Answer Choices:
A. r2​
B. r
C. not a side of an inscribed regular polygon
D. 2r3​​
E. r3​
Solution:
XY is the perpendicular bisector of AB.∴MB=MA.∠BMA is inscribed in a semi-circle and thus is a right angle.
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