A right triangle with a red and yellow square attached. Two circular arcs centered in the triangle vertices. What is the area of the orange rectangle in terms of red and yellow?
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House of Orange
Tag: circle
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Out of proportion
An equilateral triangle containing a parallelogram, another equilateral triangle and a circular arc that is tangent in its base vertices. What is the proportion pink : blue?
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Circular architecture
An equilateral triangle and two circles. The centre of the right circle is the triangle side midpoint. Both circle intersections lie on a triangle side. Prove that the three red circular arcs are congruent.
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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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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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The sacrosanct circles
Two tangent circles and two tangent line segments meeting in a point on the outer circle. The tangency points are connected by a line segment of length x. What’s x in terms of a and b?
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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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Squaring the circle
Two perpendicular squares inside a circle. The circle centre is located on the side of one square. The line segment connecting two vertices has length a. What is the circle area?
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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 yardstick
A rectangle containing a circle and a line segment connecting the top side to the bottom tangency point. What is its area in terms of lengths a and b?