Math, asked by Anonymous, 1 year ago

Prove that the circle drawn on any one of the equal sides of an isosceles triangle as diameter, bisects the third side of the triangle.

Answers

Answered by dainvincible1
3
Let ABC is the isosceles triangle where AB = AC 
The circle drawn on AC as diameter intersects BC at D
From Circle theorem we know that the angle inscribed on semicircle is 90 degree
Hence angle ADC is 90 degree 
So we have angle ADB is 90 degree
This gives Δ ADC and Δ ADB are right angled triangle.
We have hypotenuse =AB=AC and AD common leg
Two right triangles are congruent if the hypotenuse and one corresponding leg are equal in both triangles.
as.. Δ ADC ΔADB are congruent
∴ BD=DC
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