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 queen
Tag: quadrilateral
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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?
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Z
A green quadrilateral of which two sides are tangent to a quarter circle of radius r. What is its area?
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The flying saucer
A quarter circle with four chords. What is the proportion purple : gold?
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The freight elevator
Four points A, B, C and D form a quadrilateral. Prove that it is a rectangle if and only if for an arbitrary point P we have PA2+PC2=PB2+PD2.
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Brothers in arms
The tangency points of two tangents of a circle are connected. Three perpendiculars are drawn from a point on the circle, of which two have a given length. What’s the proportion red : yellow?