Two similar triangles ABC and EBD. Two line segments meet at point F. Prove that ABFC and EBDF are cyclic quadrilaterals.
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The same vein
Tag: circle
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Baby steps
The edges of a cyclic quadrilateral extend to two intersections. O is the circle centre. The two diagonals intersect inside the circle. What is the angle α?
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The party hat II
An equilateral triangle with a circular arc through its red centre and two vertices. If the yellow area equals the green one, what’s the angle α?
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Holes in my heart
The heart is divided into right triangles, each of which contains a blue circle. What is the total circumference of the blue circles in relation to the green perimeter and the lengths of the purple and orange lines in the centre?
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The crosshairs
A regular pentagon and two semicircles. Prove that they are orthogonal, i.e. the tangents in the intersection point are orthogonal.
Some chords and segments inside a semicircle. What is the ratio of red to blue?
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Three dome home
How does the white area inside the big semicircle compare to the combined white areas of the 3 smaller semicircles below it? Equally coloured semicircles are congruent.
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The basketball court
An orange circle is squeezed inside a rectangle. Show that no matter how the blue point moves on the circle, the derived points Q and P will satisfy |QL| = |KP|.
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Circle sandwich
The red and green child-circles squeeze their father (the blue circle) in the back seat while their mother drives. Show that the orange points where the children sit and where the children are squeezing their father are concyclic.
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In the red
Two congruent semicircles with their centres and a chord. Prove that the two red triangles are congruent as well.