Express the circle area in terms of the isosceles triangle area A and its side length a.
Author: Marshall W. Buck
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Launch the ball
Tag: circle
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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?
Author: Marshall W. Buck
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The small cog
Two circles, a rectangle and two line segments. Prove that the red points are collinear.
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Bond of union
Two intersecting circles with two inscribed triangles and two line segments through an intersection point. Prove that the triangles are similar.
Co-author: Marshall W. Buck.
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The three-body problem
Three coloured unit disks are placed so that they have a common (3-way) intersection, but none of the disks covers the intersection of the other two disks. What is the minimum radius of the disk that would cover all intersections at once, in all cases?
Cooperation with Marshall W. Buck.
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A tight squeeze
Two intersecting circles inside a rectangle and a line segment connecting vertex, intersection point and tangency point. What’s the angle α?
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The right position
A triangle, its incircle and a right triangle. The circle centre is shown in blue. Prove that the tangency points and right triangle vertex are collinear.
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Tumbler doll II
Three squares and a circle. The red point is a common intersection of two square sides and the circle. What is blue : green?
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Circle dancing
Start with a blue triangle, and form the green triangle whose vertices bisect each circular arc connecting blue vertices. Similarly, make the red triangle from the green, and the orange triangle from the red. Prove the triangle becomes equilateral in the limit.
Author: Marshall W. Buck.
Categories
The film projector
A square and two congruent circles with three common tangents. What’s yellow : red?