Three circles (two with centre) and four line segments. Prove that, if the small circle is orthogonal to both wheels, then the wheels are also orthogonal to each other.
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The odd bicycle
Tag: angle
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Sixtynine
A regular hexagon shares a side with a regular nonagon. What’s the angle α?
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Kitty corner crossing
What is the green angle α between the cross ways?
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Angle chase
Two triangles are placed as shown. What is the angle α?
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A mild temperature
Two squares and a diagonal. What’s the angle α?
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Polar opposites
The polar lines for a point E with respect to the blue and green circles intersect at a point T. Show that the orange circle with diameter ET intersects the other circles orthogonally.
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The Grand Fir
A triangle, its circumcircle, circumcentre and two altitudes. What’s the angle α?
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Baby brother II
Three squares and three angles. What is the angle α?
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Squares connected
Two squares, one of which has an extended side. Prove that the three red vertices are collinear.
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Parallel roads
The cyclic quadrilateral FCDI, with points K such that DK perp to FI and J such than IJ perp to CD. Show that JK is parallel to FC.