What Is This Point?

Geometry Level 5

Let ABC\triangle ABC be an acute angled triangle with side lengths AB=5,BC=7,CA=8.AB= 5, BC= 7, CA= 8. Let DD be the foot of perpendicular from AA to BC,BC, and let OO be its circumcenter. The feet of perpendiculars from OO to ABAB and ACAC intersect ADAD at points QQ and PP respectively. Let SS be the circumcenter of OPQ.\triangle OPQ. If cos(CAS)=abc\cos (\angle CAS) = \frac{ a \sqrt{b} } { c} for some square free integer bb and coprime positive integers aa and bb, then find a+b+ca+b+c .

Details and assumptions
- This problem is adapted from an ARO 10th grade geometry problem.

×

Problem Loading...

Note Loading...

Set Loading...