72. A variable parallel is drawn to the base of a triangle ABC, meeting AB, AC in Q, R; BM, CN are perpendicular to the bisector of the vertical angle. If QM, RN meet at P, it is required to prove that the circumcircle of PQR touches the inscribed circle of ABC and also one of the exscribed circles

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72. A variable parallel is drawn to the base of a triangle ABC, meeting AB, AC in Q, R; BM, CN are perpendicular to the bisector of the vertical angle. If QM, RN meet at P, it is required to prove that the circumcircle of PQR touches the inscribed circle of ABC and also one of the exscribed circles

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72. A variable parallel is drawn to the base of a triangle ABC, meeting AB, AC in Q, R; BM, CN are perpendicular to the bisector of the vertical angle. If QM, RN meet at P, it is required to prove that the circumcircle of PQR touches the inscribed circle of ABC and also one of the exscribed circles

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72. A variable parallel is drawn to the base of a triangle ABC, meeting AB, AC in Q, R; BM, CN are perpendicular to the bisector of the vertical angle. If QM, RN meet at P, it is required to prove that the circumcircle of PQR touches the inscribed circle of ABC and also one of the exscribed circles

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72. A variable parallel is drawn to the base of a triangle ABC, meeting AB, AC in Q, R; BM, CN are perpendicular to the bisector of the vertical angle. If QM, RN meet at P, it is required to prove that the circumcircle of PQR touches the inscribed circle of ABC and also one of the exscribed circles

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