Blue and green circles with tangents. The green tangent line goes through the blue tangent point and the points IJH are collinear. Show that the blue and orange lines are parallel.
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Rolling level
Tag: circle
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The Cheshire Cat grin
What is the total area of the green teeth relative to the large circle area? (Assume the inner circle radius is 80% of the outer. The 32 lines forming the tooth sides are concurrent, and spaced at equal angles apart.)
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The high-water mark
Two equilateral triangles on a blue line segment. Prove that the red line segment is parallel to it.
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Little red square
Two squares and a circle. The line through the big square centre and small square vertex is tangent to the circle. What is the red area?
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All-seeing eye
If the radius shrinks by the factor 1/2 for each smaller circle, what fraction of the whole area is represented by all the blue crescents (separated by the red crescents)? Assume the circles keep going inward forever.
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The ball pit
Two rectangles contain 6 congruent circles. The common rectangle side passes through the top centre. What’s yellow : red?
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Cycling of tangents
Four circles share one point. The quadrilateral has vertices which are intersections of pairs of circles, and three of its coloured edges are tangent to the circle of the same colour. Show that the fourth edge is also tangent to its circle.
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Shine your light
A quarter circle of radius 1, a rectangle touching the circle in an arbitrary point and a yellow quadrilateral. What is the minimal perimeter of this quadrilateral?
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Launch the ball
Express the circle area in terms of the isosceles triangle area A and its side length a.
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The hemispheric battle
C fires at city B and D fires at city A, but their rockets collide in mid-air and fall into the ground at F. Then C fires a laser bouncing off the ground at F at the same angle as incidence. Will the laser beam hit combatant D?