Triangle ABC is an isosceles triangle , such that AB=AC and point D is the mid point of AC. A circle is drawn taking BD as diameter , which intersect AB at E
Prove that
AE = AC/4
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1 Answers
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From the question,BD is the diameter and AC is a tangent.
Therefore,angle BDA=angle BDC=90°
Also, AD is median.Thus by SAS congruence,triangle ABD is congruent to triangle ACD.
Therefore AB=BC
Thus triangle ABC is equilateral.
If we join ED, angle DEB is 90°[angle in semicircle]
angle A=60°
cos A=AE/AD=1/2
→AE=AD/2
→AE=(AC/2)/2
→AE=AC/4
Thus proved
There are many other ways to do this sum as well....
- Arkadyuti Banerjee Thanks. I couldn't solve the same sum.Upvote·0· Reply ·2013-04-25 09:15:37
