In triangle PQR QM perpendicular to PR, RN perpendicular to PQR, H is ortocentre of triangle PQR then PNHM is -----
To determine the shape of the quadrilateral PNHM, we can start by analyzing the given information and using some properties of triangles.
First, let's recall the definition of an orthocenter. The orthocenter of a triangle is the point where all three altitudes of the triangle intersect. An altitude is a line segment drawn from a vertex of the triangle that is perpendicular to the opposite side.
In the given triangle PQR, we know that QM is perpendicular to PR, which means that QM is an altitude of triangle PQR originating from the vertex Q. Similarly, RN is perpendicular to PQR, making RN an altitude originating from the vertex R.
Since H is the orthocenter, we can conclude that H is the point of intersection between QM and RN.
Now, let's visualize the triangle PQR with its altitudes and the orthocenter H:
H
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Q---------M
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R
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N
Based on this diagram, we can see that the quadrilateral PNHM is formed by the segments PQ, QM, MR, and RP.
Considering the given properties (namely, the orthocenter and the altitudes), we find that PNHM is a cyclic quadrilateral. A cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. In this case, the circle is the circumcircle of triangle PQR.
Therefore, we can conclude that the shape of quadrilateral PNHM, given the information provided, is a cyclic quadrilateral.