Two regular pentagons share a vertex. What’s the angle α?
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The happy couple
Month: July 2024
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The center falls apart
In a right triangle ACB show that the incircle touches sides AC and CB in points that are vertically lined up with the centers of the incircles for ADC and BDC. Furthermore, show that the red and green distances are equal.
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The beach ball
What fraction of the regular dodecagon is red?
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Conway circular area
A triangle with sides a, b, c, when extended to whiskers of opposite side length, forms the “Conway Circle”. What is the area of the circle in terms of the expressions a+b+c, ab+bc+ca, abc of the side lengths a, b, c.
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Family constellation
Two equilateral triangles on a line. Prove that the blue triangle is equilateral as well.
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Tipping point II
Two regular pentagons share a vertex. What’s the angle α?
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All connected
Four coloured rectangles and three line segments. Prove that the three line segments are concurrent.
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Drilling site
A blue flagpole is erected near a drilling site. Lines are drilled perpendicular to the flagpole guy wires and meet at the bottom of the orange drilling pipe. What is the ratio of distances green to red?
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Rolling along
Tangents to the blue circle (ABC) intersect at a point K, and the line AK intersects (ABC) at H. D is the midpoint of BC. Show that the green circle (DHB) is tangent to the line AB.
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Ten to nine
Two triangles and one incircle with its centre and tangency points. Prove that the triangles are similar.