Let A B be a diameter of a circle and let C be a point on the segment A B such that A C: C B=6: 7 . Let D be a point on the circle such that D C is perpendicular to A B . Let D E be the diameter through D . If [X Y Z] denotes the area of th

Question

Let A B be a diameter of a circle and let C be a point on the segment A B such that A C: C B=6: 7 . Let D be a point on the circle such that D C is perpendicular to A B . Let D E be the diameter through D . If [X Y Z] denotes the area of the triangle X Y Z . Find [A B D] /[C D E] to the nearest integer.

Quantrex Academy · Accepted Answer

Correct answer: 13

aligned & C D= r^2- r^2 13^2 = r 13 12 14 & = 1 12 14 = 1 12 14+1 & C P C D = = C P r 13 12 14 = 1 12 14+1 & C P= r 12 14 13 12 14+1 & |A B D| |C D E| = 1 2 (2 r) r 13 12 14 1 2 (2 r) r 13 12 14 12 14+1 = 12 14+1 =13 aligned

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