04
Sep
Question 10: If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.
Prerequisite
It is bit tricky question to solve (not difficult though). Such questions are generally proved by assuming the other way and proving the assumption wrong. For example, in this question we assumed that the point of intersection does not lie on the third side of the triangle and then proved this assumption wrong. To prove the theorem, we used one very common property of circles – angle in a semicircle is always a right angle.
Angle in a semicircle is a right angle
Chapter 10 – Circles
