Problems

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Found: 4

The bisector of the outer corner at the vertex C of the triangle ABC intersects the circumscribed circle at the point D. Prove that AD=BD.

The vertex A of the acute-angled triangle ABC is connected by a segment with the center O of the circumscribed circle. The height AH is drawn from the vertex A. Prove that BAH=OAC.

The vertex A of the acute-angled triangle ABC is connected by a segment with the center O of the circumscribed circle. The height AH is drawn from the vertex A. Prove that BAH=OAC.

From an arbitrary point M lying within a given angle with vertex A, the perpendiculars MP and MQ are dropped to the sides of the angle. From point A, the perpendicular AK is dropped to the segment PQ. Prove that PAK=MAQ.