Two tangent circles and a third circle touching the line segment connecting their centres in the tangency point. Prove that the red points (centre and two intersection points) are collinear.
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Wheels in motion
Tag: circle
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It’s complicated
A circle, a semicircle and several triangles. The black points are tangency points. What proportions have the line segments a : r : b?
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The odd couple
A semicircle with two inscribed triangles The tangency points of the incircle of the bigger triangle are shown. What is the triangle area proportion orange : blue?
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Blazing hot
A circle inscribed in a triangle inscribed in a semicircle. The line segment through two tangency points meets a radius at the semicircle circumference. What is the angle α?
A square containing a rectangle and a tangent quarter circle. What fraction is orange?
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Camera obscura
A quarter circular room is covered with mirrors. A ray of light is emitted from one corner and reflected somewhere on the opposite wall, then on the arc, before reaching the adjacent wall at a point a distance a from the light source and b from the circle centre. What is the maximum of a/b?
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The pine forest
A square containing a quarter circle. What’s the proportion blue : brown : green?
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The Eightfold Path
A semicircle, a square and an isosceles triangle. What’s the angle α?
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Tomba La Bomba
Three regular hexagons inside a circle. Two shared vertices and five vertices on the circle. What’s red : green?
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The augmented chord
A circle with four chords. What is the length of line segment x in terms of lengths a and b?