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.

Question

cdquestions Admin · Accepted Answer

Consider a ∆ABC.  Two circles are drawn while taking AB and AC as the diameter.  Let they intersect each other at D and let D not lie on BC.  Join AD.  ∠ADB = 90° (Angle subtended by semi-circle)  ∠ADC = 90° (Angle subtended by semi-circle)  ∠BDC = ∠ADB + ∠ADC = 90° + 90° = 180°  Therefore, BDC is a straight line and hence, our assumption was wrong.  Thus, Point D lies on third side BC of ∆ABC.

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

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.

Solution and Explanation

Top CBSE Class IX Mathematics Questions

Top CBSE Class IX Questions