Problem: In a circle with center at O and radius r, chord AB is drawn with length equal to r (units). From O a perpendicular to AB meets AB at M. From M a perpendicular to OA meets OA at D. In terms of r the area of triangle MDA, in appropriate square units, is:
Answer Choices:
A. 163r2β
B. 16Οr2β
C. 8Οr22ββ
D. 32r23ββ
E. 48r26ββ
Solution:
Since AB=r, the measure of angle A is 60 (degrees) and AM=21βr. In right triangle MDA, since AM=21βr and the measure of angle AMD is 30(degrees), AD=41βr and MD=41βr3β.
Therefore, the area of β³MDA=21β(AD)(MD)=21ββ 4rββ 4r3ββ=32r23ββ.