A regular hexagon is divided in four triangles and one quadrilateral. Express the hexagon area in terms of areas A, B and C.
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Tip of tipi
Category: Intermediate
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Criss cross chords
The blue unit circle has a diameter and several colored chords. The red chord bisects the angle between the green chords. Express the sum of the green chords in terms of the red and purple chords.
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Circular cuts
The blue parallelogram’s vertex C lies on a green circle that intersects the diagonal BC at J. What is the length of the red segment?
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Centre stage
A square with its centre and a right angle. What’s ad-bc?
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The helmet visor
A quarter circle and a semicircle with several line segments, one of which is tangent to the semicircle. What is the area proportion semicircle : quarter circle?
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Man in the middle
Three equilateral triangles share a vertex. What is the area of the blue one in terms of green and red?
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The fourth circle
Three circles and a line segment connecting three intersections. Prove that the three centres and the common intersection are concyclic.
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Bicyclic transport
EHF is tangent to the purple circle at E, and EN is tangent to the red circle at N. A and C are the circle centers. A blue rectangle has three corners HEC and the point A on one side. What is the ratio of areas, green square to orange quadrilateral?
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Locus pocus II
What is the locus of points P for which perpendicular lengths (red=l, green=n, purple=m) to the sides of an isosceles triangle satisfy the condition red*green = purple2?
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The center falls apart
In a right triangle ACB show that the incircle touches sides AC and CB in points that are vertically lined up with the centers of the incircles for ADC and BDC. Furthermore, show that the red and green distances are equal.