Question
Thu February 14, 2013 By: Shubham Deshpande

in tri. ABC ab=ac a circle passes through b and touches ac at the mid P the circle intersects ab in the piont Q prove that bq=aq

Expert Reply
Sun February 17, 2013
There is some mistake in the question you posted. BQ and AQ cannot be equal. Infact, the question should be to prove 4AQ = AB. 
And, this can be proved as follows:
 
 
AC is the tangent and AQ is a secant to the circle.
So, AQ x AB = AP2
AQ x AB = 1/4AC2
as P is the mid point of AC
Also, AB = AC
So, we get,
4AQ = AC
or 4AQ = AB
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