BMO 2006/7 circles question

Two touching circles S and T share a common tangent which meets

S at A and T at B. Let AP be a diameter of S and let the tangent

from P to T touch it at Q. Show that AP = PQ.

If you have solved it then please give me a hint(don't post the full solution).

Thanks in advance.

Re: BMO 2006/7 circles question

Quote:

Originally Posted by

**abhishekkgp** Two touching circles S and T share a common tangent which meets

S at A and T at B. Let AP be a diameter of S and let the tangent

from P to T touch it at Q. Show that AP = PQ.

If you have solved it then please give me a hint(don't post the full solution).

Thanks in advance.

1. **Draw a sketch!**

2. Prove(!) that the described situation is only possible if the 2 circles are congruent.

3. Prove that the 2 diameters and the tangent segments consequently form a square.

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Re: BMO 2006/7 circles question

Quote:

Originally Posted by

**earboth** 1. **Draw a sketch!**

2. Prove(!) that the described situation is only possible if the 2 circles are congruent.

3. Prove that the 2 diameters and the tangent segments consequently form a square.

I have attached a sketch. The two circle S and T drawn are not congruent but i still get AP=PQ.