TWO CIRCLES S1 AND S2 ARE TANGENT AT P. A COMMON TANGENT, NOT THROU...

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Toán ĐỀ THI OLYMPIC TOÁN HỌC QUỐC TẾ BMO NĂM 2020

3. Two circles S

1

and S

2

are tangent at P. A common tangent, not through P,

touches S

1

at A and S

2

at B. Points C and D, on S

1

and S

2

respectively, are

outside the triangle APB and are such that P is on the line CD.

Prove that AC is perpendicular to BD.