A red equilateral triangle and its circumcircle. Prove that the blue triangle is also equilateral.
Tag: triangle
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Interlocked triangles
Do the blue, green, and orange triangles have the same shape?
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Seeing double II
A right triangle is divided in two triangles by an altitude. The three incircles are shown with three tangency points. Prove that the two red line segments are congruent.
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Sunrise over green mountain
An acute triangle mountain ABC has altitudes BE and CF. The dotted tangent lines to the sunny circumcircle (AEF) at E and F intersect at a point M. Show that M is on the mountain’s base BC.
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The silly walk
A circle and several triangles. Prove that the green triangle is isosceles.
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The sun hat
Two triangles share a circumcircle and vertex, with one edge of the orange triangle containing the feet of two of the altitudes of the blue triangle. Show that the orange triangle is isosceles.
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Stay centred
Two squares share a vertex. Prove that the red point is the circumcentre of the red triangle.
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Uneasy the head
The green zigzag crown segments would extend through either B or C. Show that the arcs along the top are equally spaced.
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Giant’s shoulder II
Three equilateral triangles share three vertices. What is blue : red?
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Falling in
Start with an acute triangle and form a new triangle from the points of tangency of its inscribed circle. Continue this process to make make the triangle with blue vertices. What is the maximum possible angle at a blue vertex?