Two squares and some line segments. Find the relation between the angles α and β.
Tag: triangle
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The belly button
A quarter circle with a right triangle. Prove that the red point is the incentre of this triangle.
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Fair scoop
What is the ratio of areas purple : orange if the cone angle is 45°, and the circular arc is a semicircle?
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Mother’s umbrella
A circle containing two internally tangent circles. Prove that the red triangle is isosceles.
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Antennas above and below
The triangle ABC has orthocentre H, so that HA is an antenna above the green hill. The rectangle BCDE is inscribed in the circumcircle (ABC). Show that HA = CD = BE.
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Six six four
Two regular hexagons and a square. What’s the angle α?
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Two medians and one side
A triangle has sides a,b,c and the medians d,e,f ending at those sides, respectively. Given only the lengths (b,d,e) construct the triangle (a,b,c). (Start with a triangle with side lengths determined in some manor from the given 3 lengths.)
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Triangle offspring
Four equilateral triangles. Prove that the three black line segments are concurrent.
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Crashing the kite
The orange lines are parallel, the purple lines are parallel, the dotted gray lines intersect the base at equal distances. What is the ratio of areas of the blue and green triangles?
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Unring a bell
A square and an equilateral triangle. What’s the angle α?