A non-isosceles triangle with a red cevian and three line segments to a point on the cevian. Prove that this point is the incentre of the triangle.
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To the core
Tag: triangle
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The seventh bell
A regular hexagon shares a vertex with an equilateral triangle of area 7. What is the area of the hexagon?
A square contains a yellow right triangle with an area of 11. What is the square’s area?
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The erratic spider
A square with several line segments. Prove that the blue ones are parallel.
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Almost sunk
A square contains a right triangle. What fraction is red?
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The side mirror
An isosceles triangle and an external point with three line segments. Prove that the red points form a cyclic quadrilateral.
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The Santos conundrum
A triangle is divided by three line segments into five smaller triangles. What is its area expressed in terms of areas A, B and C?
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Two brotherly pines
Three triangles are glued together. The green ones are based on a common line. What’s the angle α?
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A light packing
A triangle containing two congruent squares. Each square has 1/3 the perimeter and 1/6 the area of the triangle. What’s the triangle side length proportion a : b : c?
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Going halfway
A regular hexagon contains a diagonal, a green equilateral triangle and a red triangle. Prove that the latter is isosceles.