Draw line segments PA and PC. This forms right triangle APC with a right angle at P. Also, PB is perpendicular to AC, so 3 right triangles are formed: APB, PBC, and APC. Note that all of these triangles are similar to each other.
Statement 1: AC=29. Let BC=x and AB=29-x. PBC is similar to ABP, so 10/x=(29-x)/10 or 100=29x-x^2. Solving this gives x=25 or x=4. However, BC is clearly longer than the radius, which is 14.5, so x=25, and AC=4. SUFFICIENT.
Statement 2: BC=25. let AB=x. using similar triangles again, we can set up the ratio x/10=10/25. Solving for this gives x=4. SUFFICIENT.
Ans: D
Geometry Problem
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