A square with its diagonal. Prove that the three red points are collinear.
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Distant Alp II
Month: May 2024
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The whirligig
The green blades form a bowtie that is symmetric about the vertical orange line g. Show that the blue horizontal line f, the red circle (ADE), and the purple circle (AOC) are concurrent. (Assume that COB and AOD are colinear.)
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Rectangle offspring
Three rectangles of which the blue and the pink one are similar. Prove that the yellow rectangle is also similar.
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Carom billiards
Three congruent circles have a common intersection. Prove that the red intersection is the orthocentre of the triangle.
Blue and orange concentric circles intersect a vertical line in green dots. Show that the dots are equally spaced, given that the red intervals shown are of equal length. (The largest circle has radius 2u.)
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Equilateral linkage
Given 3 points A, B, C, define G so CG=CB and angle GCB is 120 degrees. Define M as the midpoint of side CH of the parallelogram CGAH. The green equilateral has side CM and the purple equilateral has side MB. Is AJK also equilateral?
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Pushed together
A square containing two semicircles. The red line segment is a common tangent. What fraction is green?
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Lifting the veil
A blue triangle and a red rectangle with an extended side. Prove they have equal area.
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The line up
Two semicircles share a common diameter HB. Point A in the upper half projects to E along the diameter, and to G along the line segment BC. F is the midpoint of AC. Show that FEG are collinear.
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Spotlight II
A square is divided in several triangles and quadrilaterals. What is yellow : red?