1) A, B, C, and D are points on a circle, and segments AC and BD intersect at P, such that AP = 8, PC = 1, and BD = 6. Find BP, given that BP < DP.
2) In 4ABC, AB = 3 and BC = 5. Find the number of possible integer values of CA. [Disclaimer]: In this class, we do not consider degenerate triangles (i.e. a triangle whose area is 0).
3) In obtuse 4ABC, AB = 3 and BC = 5. Find the number of possible integer values of CA
+1486 1) A, B, C, and D are points on a circle, and segments AC and BD intersect at P, such that AP = 8, PC = 1, and BD = 6. Find BP, given that BP < DP.
Let AC be a side of an inscribed square. Let O be a center of a circle, and N is the intersection point of BD and CO.
AP = 8 PC = 1 BD = 6 ∠(CPN) = 45°
PN = sqrt [(PC)² /2] = sqrt(1/2) = [ sqrt(50)] /10 = sin(45°) = cos(45°) = 0.707106781
BP = ( BD/2 ) - PN = 2.292893219 units 
