3/25/2023 0 Comments Kite quadrilateral![]() ![]() In a cyclic orthodiagonal quadrilateral, the anticenter coincides with the point where the diagonals intersect.Its area can be expressed purely in terms of its sides.įor any orthodiagonal quadrilateral, the sum of the squares of two opposite sides equals that of the other two opposite sides: for successive sides a, b, c, and d, we have a 2 + c 2 = b 2 + d 2. An orthodiagonal quadrilateral that is also equidiagonal is a midsquare quadrilateral because its Varignon parallelogram is a square. The square is one such quadrilateral, but there are infinitely many others. Orthodiagonal equidiagonal quadrilaterals in which the diagonals are at least as long as all of the quadrilateral's sides have the maximum area for their diameter among all quadrilaterals, solving the n = 4 case of the biggest little polygon problem. Ī rhombus is an orthodiagonal quadrilateral with two pairs of parallel sides (that is, an orthodiagonal quadrilateral that is also a parallelogram).Ī square is a limiting case of both a kite and a rhombus. The kites are exactly the orthodiagonal quadrilaterals that contain a circle tangent to all four of their sides that is, the kites are the tangential orthodiagonal quadrilaterals. 6 Infinite sets of inscribed rectanglesĪ kite is an orthodiagonal quadrilateral in which one diagonal is a line of symmetry.5 Properties of orthodiagonal quadrilaterals that are also cyclic.2.1 Comparison with a tangential quadrilateral. ![]()
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