Vietnam TST 2001
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- Posts:66
- Joined:Tue Mar 20, 2012 12:52 am
Two circles intersect at A and B.One of their common tangents touches the circles at P and Q.Tangents to the circumcircle of APQ at P and Q intersect at S.Let the reflection of B wrt PQ is H.Prove that A,S,H is collinear.
- zadid xcalibured
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Re: Vietnam TST 2001
at first prove that H lies on the circumcircle of APQ.then angle chasing yeilds H lies on the A symmedian.but we know AS is the A symmedian.actually AB is median.if AB cuts PQ at M.then PM=QM from power of point and radical axis.angle chasing helps as we have alternate segmental angles.
Re: Vietnam TST 2001
$\text{My solution}$:
"Questions we can't answer are far better than answers we can't question"