To the circle x 2 + y 2 = 4 two tangents are drawn from P ( − 4 , 0 ) which touch the circle at T 1 and T 2 and a rhombus P T 1 P ′ T 2 is completed. Circumcentre of the triangle P T 1 T 2

Question

To the circle x 2 + y 2 = 4 two tangents are drawn from P ( − 4 , 0 ) which touch the circle at T 1 ​ and T 2 ​ and a rhombus P T 1 ​ P ′ T 2 ​ is completed. Circumcentre of the triangle P T 1 ​ T 2 ​ is at

TestHub · Accepted Answer

P T 2 ​ = P T 1 ​ = ( − 4 ) 2 + 0 2 − 4 ​ = 2 3 ​ . Since ∠ P T 1 ​ O = ∠ P T 2 ​ O = 9 0 ∘ , the circumcentre of triangle P T 1 ​ T 2 ​ is the midpoint of PO = ( 2 − 4 + 0 ​ , 2 0 + 0 ​ ) = ( − 2 , 0 ) .

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