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CBSE Class 9 Answered

Prove that the circle drawn on any one of the equal side of an isosceles triangle as diameter , bisects the third side.
Asked by krishanmunjal019 | 23 Jan, 2019, 06:09: AM
answered-by-expert Expert Answer
Figure shows an isoceless triangle ABC with AB = AC. A circle drawn with AB as diameter intersects third side BC at D.
 
Let us join A and D to make a line segment AD.
 
Since AB is diamter of circle, angle ADB subtended by diameter is 90°.  Hence AD is perpendicular to BC.
 
If we consider two right triangles ADB and ADC, it is possible to prove that both are congruent,
because both hypotenuses are equal and AD is common side.
Hence BD = DC.
 
Also, in a isoceless triangle, perpendicular line drawn from the common vertex of equal sides to the third side will bisect the third side.
Answered by Thiyagarajan K | 23 Jan, 2019, 08:18: AM

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