An arbitrary point B on the unit circle is reflected in the y-axis to give B’. D is the intersection of BC and AB’. Prove it lies on the red hyperbola.
Puzzle creator: Matthew Arcus.
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A hyperbolic style
Tag: circle
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Shooting the moon
Show that the blue dots are concyclic and also the orange dots are concyclic.
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The tipi entrance
A semicircle with three tangents. Prove that purple : green = red : yellow.
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Encircling an anvil
Two equilateral triangles, one upside down, have boundaries meeting at 4 points, 3 of which are marked in red. Show that the circle through the red points also passes through the centre point of the blue triangle.
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The Swiss cheese
A triangle containing two congruent semicircles. The four tangency points are shown. What fraction is yellow?
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Roly poly doll
Two circles with diameters (green and orange) from one of the intersection points. Show that the other intersection point of the circles is on the (purple dotted) line connecting the other ends of the diameters.
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Tilted hourglass III
A regular hexagon, a circle through its red centre and two line segments. What’s blue : orange?
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The same vein
Two similar triangles ABC and EBD. Two line segments meet at point F. Prove that ABFC and EBDF are cyclic quadrilaterals.
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Baby steps
The edges of a cyclic quadrilateral extend to two intersections. O is the circle centre. The two diagonals intersect inside the circle. What is the angle α?
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The party hat II
An equilateral triangle with a circular arc through its red centre and two vertices. If the yellow area equals the green one, what’s the angle α?