August 2018 Geometry#4 (Previous problem corrected)
Chords and intersect at right angles inside the circle centered at
If and then find
Note: The diagram is not drawn to scale.
The answer is 483.
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1 solution
Using cosine law, we get cos(EBO) = (-OE^2+EB^2+OB^2)/(2 * EB * OB) = (-49+81+121)/(2 * 9 * 11) = 0.773 Angle (EBO) is 39.40°
Let K be the projection of O on AB (K is the midpoint of AB). BK = 11 cos(EBO) = 8.5
Let F be the projection of O on EC. OF = KE = BE-BK = 0.5.
DF^2 = OD^2 - OF^2 = 121 - (0.5)^2 = 120.75. DC= 2 * DF, so DC^2 = 4 DF^2
DC^2 = 483.