Latest Maths Olympiad Aptitude Question SOLUTION: Let ABC be a triangle in which no angle is 90◦. For any point P in the plane of the triangle, let A1,B1,C1 denote the reflections of P in the sides BC,CA,AB respectively. Prove t

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(#M40021935) MATHS OLYMPIAD question GEOMETRY Keep an EYE

Let ABC be a triangle in which no angle is 90◦. For any point P in the plane
of the triangle, let A1,B1,C1 denote the reflections of P in the sides BC,CA,AB
respectively. Prove the following statements:
(a) If P is the incentre or an excentre of ABC, then P is the circumcentre of A1B1C1;
(b) If P is the circumcentre of ABC, then P is the orthocentre of A1B1C1;
(c) If P is the orthocentre of ABC, then P is either the incentre or an excentre of
A1B1C1.

Asked In Maths Olympiad MAN (10 years ago)

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