A triangle with its incircle and three cevians. The tangency points and incentre are shown. Find the relation between the angles α, β and γ.
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Wheel of fortune II
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In times out
What is the area of the green rectangle, which has sides tangent to the incircle and circumcircle of a triangle with side lengths a, b, c.? (Write the answer as a multiple of a quotient of two elementary symmetric functions in a, b, c.)
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Video: Hats off
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The Bedouin tent
A semicircle and a triangle of which one side is tangent to the semicircle. What is the angle α?
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Video: The ceiling lamp
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Shots in the dome
A beam from the top of one tower cuts through the dome, reflects off the ground, and hits the top of the other tower. Show that the line connecting the orange dots, the line connecting the blue dots, and the ground line are concurrent.
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Four six four
A regular hexagon and two similar rectangles. What fraction is green?
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Video: Six four
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Eclipsing earth
Two circles with their centres. The quadrilateral ABCD is cyclic and has two sides tangent to the small circle. Prove that BD is also tangent.
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Wedging the circle
Four similar triangles share one circle as incircle or excircle. Show that orange dotted lines must be concurrent.