Q: 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.
Given: circles are drawn taking two sides of a triangle as diameters.
Construction: Join AD.
Proof: AB is the diameter of the circle and ADB is formed in a semi-circle.
ADB = ........................1(angle in a semi-circle)
Similarly,
AC is the diameter of the circle and ADC is formed in a semi circle.
ADC = ........................2(angle in a semi-circle)
From 1 and 2, we have
ADB+ADC=+=
ADB and ADC are forming a linear pair. So, BDC is a straight line.
Hence, point D lies on this side.