An isosceles triangle and an external point with three line segments. Prove that the red points form a cyclic quadrilateral.
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The side mirror
Tag: quadrilateral
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The inner parallel
A cyclic quadrilateral with its diagonals and two altitudes. Prove that AB is parallel to EF.
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Ceteris paribus
Three circles with their centres and a triangle ABC. Given that D is the midpoint of BC, prove that quadrilateral ABEF and triangle ECF have both equal perimeter and equal area.
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The hand fan
Three congruent triangles constitute a quadrilateral. What’s red : blue?
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The queen
A cyclic quadrilateral with extended sides and two tangents forming an angle γ. What is γ in terms of α and β?
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The leftward lean
Two triangles form a quadrilateral. What’s the total orange area?
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We are equal
A quadrilateral with its diagonals. What’s the angle α?
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The square of Amaresh
A right triangle having semicircles along its perpendicular sides and two smaller inscribed circles. Prove that the orange quadrilateral is a square.
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The French kiss
Two tangent circles and two red tangent line segments. The three tangency points are shown. What is the angle β in terms of the angle α?
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Similar intention
A cyclic quadrilateral and two diagonals. What fraction of its area is blue?