A rectangle with a diameter and two inscribed squares. What is its area in terms of the square areas A and B?
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The letter box
Month: December 2021
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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?
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The tornado
A quadrilateral covers exactly half of the area of a rectangle. Find the length x in terms of a, b and c.
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The steam iron
The midpoints of the hypotenuse of a right triangle and a line segment are connected. What is the length x?
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David and Goliath
Two squares share a vertex. What’s the proportion blue : green?
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The major chord
A circle with four chords. What is the segment length x in terms of lengths a, b and c?
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The molecule
Three semicircles of which two centres are connected to corner points. What is the area X in terms of A and B?
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A close encounter
Two semicircles are tangent to each other’s diameter. Are the line segments connecting their corners parallel?
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The hawfinch
An equilateral triangle with a circle tangent to two sides. The vertices are the tangency points. What is the length proportion of line segments x : y?
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The core business
Two squares with two highlighted vertices and a centre. Proof that these points are collinear.