# 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:**

We know that an angle in a semicircle is a right angle. By using this fact, we can show that BDC is a line that will lead to prove that the point of intersection lies on the third side.

Since angle in a semicircle is a right angle, we get:

∠ADB = 90° and ∠ADC = 90°

∠ADB + ∠ADC = 90° + 90°

⇒ ∠ADB + ∠ADC = 180°

⇒ BDC is a straight line.

D lies on BC

Hence, the point of intersection of circles lies on the third side BC.

**Video Solution:**

## 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

### Maths NCERT Solutions Class 9 - Chapter 10 Exercise 10.5 Question 10:

**Summary:**

If circles are drawn taking two sides of a triangle as diameters, we have found that the point of intersection of these circles lies on the third side.