Olympiad workbookIOQMCircle
Let A B be a diameter of a circle and let C be a point on , different from A and B . The perpendicular from C intersects A B at D and at E( C ) . The circle with centre at C and radius C D intersects at P and Q . If the perimeter of the triangle P E Q is 24 , find the length of the side P Q .
Correct answer
08
Step-by-step solution
C P E Q is cyclic quadrilateral aligned & C P E Q+C Q P E=C E P Q & r(E Q+P E)=2 r P Q & 2 P Q=E Q+P E & P Q+E Q+P E=24 & P Q+2 P Q=24 & P Q=8 aligned