Mon February 27, 2012 By:

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

Expert Reply
Mon February 27, 2012
Given: ?ABC is an isosceles triangle with AB = AC. A circle is drawn taking AB as the diameter which intersects the side BC at D.
To prove: BD = DC
Construction: Join AD
Proof: ?ADB = 90°  (Angle in a semi-circle is 90°)
?ADB + ?ADC = 180°
? ?ADC = 90°
In ?ABD and ?ACD,
AB = AC   (Given)
?ADB = ?ADC  (90°)
AD = AD  (Common)
? ?ABD ? ?ACD   (RHS congruence criterion)
? BD = DC  (C.P.C.T)
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