Circles are described on the sides of a triangle as diameters. Prove t

1.	Circles are described on the sides of a triangle as diameters. Prove that the circles on any two sides intersect each other on the third side (or third side produced).
Answer» Since, AB is a diameter Then, ∠ADB = 90° ...(i) (Angle in semi-circle) Since, AC is a diameter Then, ∠ADC = 90° ... (ii) (Angle in semi-circle) Adding (i) and (ii), we get ∠ADB + ∠ADC = 90° + 90° ∠BDC = 180° Then, BDC is a line Hence, The circles on any two sides intersect each other on the third side.

Circles are described on the sides of a triangle as diameters. Prove that the circles on any two sides intersect each other on the third side (or third side produced).

Answer»

Since,

AB is a diameter

Then,

∠ADB = 90° ...(i)

(Angle in semi-circle)

Since,

AC is a diameter

Then,

∠ADC = 90° ... (ii)

(Angle in semi-circle)

Adding (i) and (ii), we get

∠ADB + ∠ADC = 90° + 90°

∠BDC = 180°

Then,

BDC is a line

Hence,

The circles on any two sides intersect each other on the third side.

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Circles are described on the sides of a triangle as diameters. Prove that the circles on any two sides intersect each other on the third side (or third side produced).

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