A circle, a semicircle, a chord and an altitude. What is the length of the latter in terms of a and b?
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The helmet
Tag: length
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The fish bowl
A circle with an inscribed triangle, a tangent and two bisected angles. What is the length proportion of the red and green line segments?
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The intersection
Two intersecting circles. Prove that the three blue line segments are of equal length.
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Two square pegs
Two squares and a circle. What is the proportion a : b?
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The other half
Three semicircles with diameters a, b and x. Express x in terms of a and b.
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The ice cream cone
A circle tangent to a triangle side and to the two other extended sides. What is its diameter?
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The red flag
Three squares of which two vertices are connected. If the red triangle has area 1.5 and the green square area 1, what is the side length x?
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The sliding square
A square of variable size inscribed in a semicircle of radius r. What is the maximum distance d of the lowest square vertex to the nearest semicircle corner?
A rectangle with two congruent circles, a semicircle and a common tangent. What is the proportion of side lengths a : b?
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And counting
A triangle containing an altitude and the inscribed circle. One tangency point is shown. The red line segments have equal length. What is the proportion of the triangle sides a : b : c?