Two semicircles contain a triangle. The centre of the right semicircle is shown. Prove that the triangle is isosceles.

# Tag: circle

## The fried egg

Two concentric circles and two tangents. What is the yellow fraction?

## The parallax effect

Two intersecting circles with a triangle that passes through their centres and an intersection point. What’s the angle α?

## The purple hat

A circle with three tangents forming an isosceles triangle. Two tangency points are shown. What is the proportion green : red?

## The queen

A cyclic quadrilateral with extended sides and two tangents forming an angle γ. What is γ in terms of α and β?

## Two hemispheres

A triangle with its circumscribed circle and a smaller intersecting circle. The two intersection points and the circumcentre are shown. What’s the proportion red : green?

## The new moon

A circle with two tangents, two chords and a secant. Prove that red and green are parallel.

## The wedge

A trapezium with its inscribed circle. Two tangency points are shown. What’s red / blue – yellow / green?

## The fish trap

Two intersecting circles and two common tangents. Prove that α = β.

## Lines in the sand

Two intersecting circles and four chords. Prove that the red chords are parallel.