Question

9. Two circles are drawn with sides AB, AC of a triangle ABC as diameters. The circles
intersect at a point D. Prove that D lies on BC.
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Answer 1

Answer:

Step-by-step explanation:

Let us suppose that there are two circles having diameter AB and AC. The circles intersect at point D.

From the figure, ABC is a triangle.

Now we have to show that D lies on the line BC.

Join A and D as shown in the figure.

Given AB and AC are the diameter of the of the circle.

∠ADB = 90 .........1 (angles in a semi circle)

and ∠ADC = 90 ........2 (angles in a semi circle)

Add equation 1 and 2, we get

∠ADB + ∠ADC = 90 + 90

=> ∠ADB + ∠ADC = 180

So BDC is a straight line.

Hense D lies on BC.

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