Question

if two circles are drawn taking two sides of a triangle as a diameter prove that the point of intersection of the circles lies on the third side​

Answer 1

Given,

Two circles are drawn on the sides AB and AC of the triangle

ABC as diameters. The circles intersected at D.

Construction: AD is joined.

To prove: D lies on BC. We have to prove that BDC is a straight line.

Proof:

∠ADB=∠ADC=90° ...Angle in the semi circle

Now,

∠ADB+∠ADC=180°

⇒∠BDC is straight line.

Thus, D lies on the BC.

solution

Answer 2

Answer:

First, draw a triangle ABC and then two circles having a diameter as AB and AC respectively.

We will have to now prove that D lies on BC and BDC is a straight line.

Proof:

As we know, angle in the semi-circle are equal

So, ∠ADB = ∠ADC = 90°

Hence, ∠ADB + ∠ADC = 180°

∴ ∠BDC is a straight line.

So, it can be said that D lies on the line BC.