Two touching circles and a common tangent. Three triangles are formed by tangency points and centres. What is the area of the green triangle X in terms of areas A and B?
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The commons
Tag: triangle
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The folded napkin
A square sheet of paper is folded symmetrically from a corner. If the fold length is 4, what is the area of the triangle formed by the other three corners?
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Twin peaks
A rectangle with three line segments. What is the proportion yellow : red?
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Pyramidion
A triangle containing a semicircle and an equilateral triangle. What fraction is golden?
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Triple dice
An equilateral triangle with three congruent squares. What’s the angle α?
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Paper hat II
Two overlapping congruent right triangles. If |AB|=15 and |BC|=7, what is the total area?
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En garde
An isosceles triangle with two altitudes dividing each other in segments of length 4 and 5. What is the total triangle area?
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Distant peaks
Two isosceles triangles and a right angle. What is the proportion green : gold?
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The Lion King II
A regular hexagon and three squares. What is the proportion yellow : brown?
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The eye mask
A right triangle with its inscribed circle. Two cevians are drawn through the circle centre. What is the circle area in terms of triangle areas A and B?