A circle with a red and a green tangent. The two tangency points are shown. Prove that the blue and red line segments are parallel.
Tag: circle
The radical
Two intersecting circles and a common tangent. The two tangency points are shown in black. Prove that the three red points are collinear.
Getting stuck
A regular pentagon and a circle through two of its vertices and its centre. What’s the angle α?
The dirty thirties
A triangle containing a semicircle and a circular sector centred in the right vertex. What is blue : green?
Scratching the surface
Three tangent semicircles and two coloured triangles. What’s the proportion yellow : green?
To the core
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.
Longing for spring
Four semicircles and three line segments. What’s the proportion yellow : orange?
Çetins circle
A square, a semicircle and six line segments. What’s the angle α?
Mother and child
Two circles, two radii and three chords. What is the length of radius x in terms of a, b and c?
The side mirror
An isosceles triangle and an external point with three line segments. Prove that the red points form a cyclic quadrilateral.