A square and a rectangle share a vertex. Two triangle areas are given. What is the total area?
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The voting pencil
Tag: triangle
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Out of focus
A semicircle with an inscribed triangle. Both circles are tangent to the semicircle, the diameter and one other triangle side. Prove that the line segment connecting the two shown tangency points is parallel to the diameter.
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The red triangle
A square containing an isosceles triangle with given side lengths. What fraction is red?
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As within, so without
A semicircle and a circle are tangent. The tangency point is shown. Prove that the two coloured triangles are similar.
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Lean on me
Two squares and two diagonals. Prove that the angles α and β are equal.
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The dolphin
Two semicircles, a tangent and an altitude to the tangency point. Prove that the red triangle is isosceles.
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The inner diamond
A triangle with side lengths a and b and an inscribed rhombus. What is the blue fraction in terms of a and b?
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Silent circle
A large triangle with one side tangent to a circle. The tangency point is the vertex of a blue parallelogram. What is the red area?
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The Suresh similarity
Two squares and a rectangle. Prove that the red triangles are similar.
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Twin balls
A semicircle with two inscribed circles tangent to an altitude. What’s the angle α?