Prove that a quadrilateral formed by joining the incentres of 4 triangles formed by diagonals of a cyclic quadrilateral is rectangle?
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The figure below is the same as above, except with the points J,K,L, M labelled and the line DB added. By definition J,K,L,M are the midpoints of their respective sides.
1 JM is the midsegment of the triangle ABD The midsegment of a triangle is a line linking the midpoints of two sides (See Midsegment of a triangle)
2 JM is half DB and parallel to it From the properties of the midsegment of a triangle
3 Likewise in triangle DBC, LK is also half DB and parallel to it From the properties of the midsegment of a triangle
4 JKLM is a parallelogram A pair of opposite sides (LK and JM) are parallel and congruent
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