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CBSE Class 9 Answered

Prove that the circle drawn on any equal side of an isosceles triangle as an diameter bisects the third side .
Asked by Vikas | 12 Jan, 2018, 10:54: AM
answered-by-expert Expert Answer
begin mathsize 16px style Construction colon space Join thin space AD
SInce space angle space in space straight a space semi space circle space is space straight a space right space angle comma
angle ADB equals 90 degree
Now comma space angle ADB plus angle ADC equals 180 degree space space space space space space left parenthesis linear space pair right parenthesis
rightwards double arrow 90 degree plus angle ADC equals 180 degree
rightwards double arrow angle ADC equals 90 degree
In space triangle ABD space and space triangle ACD comma space
AB equals AC space space space space left parenthesis equal space sides space of space isosceles space triangle right parenthesis
angle ADB equals angle ADC space space space space left parenthesis Each equals 90 degree right parenthesis
AD equals AD space space space space left parenthesis common right parenthesis
rightwards double arrow triangle ABD approximately equal to triangle ACD space space space space space left parenthesis RHS thin space congruence right parenthesis
rightwards double arrow BD equals DC end style
Answered by Rashmi Khot | 12 Jan, 2018, 12:02: PM

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