Two squares and a rectangle. Prove that red = blue.

# Category: Advanced

## Flying saucer II

If X is the midpoint of the segment connecting the centers of the upper and lower arcs, and JK is perpendicular to XH, then show that H is the midpoint of JK.

## Siamese triplet III

Three circles and a triangle. What is red : green?

## Red pistil

Three circular petals surround a red pistil which is orthogonal to each of the petals. Given the petals, construct the pistil. (You may assume that you are given a direct way to construct a tangent line from an exterior point to any circle.)

A square with two semicircles. The smaller one has an extended diameter and a tangent. What are the coordinates of the tangency point?

## Wheel in motion

A circle with its centre and two squares sharing a vertex. What’s the angle α?

## Distant Alp II

A square with its diagonal. Prove that the three red points are collinear.

## Equilateral linkage

Given 3 points A, B, C, define G so CG=CB and angle GCB is 120 degrees. Define M as the midpoint of side CH of the parallelogram CGAH. The green equilateral has side CM and the purple equilateral has side MB. Is AJK also equilateral?

## Circle a ranch brand

Connect 4 (blue) points B, C, D, E on a circle to some of the (orange) midpoints of non-adjacent arcs. (For example, C connects to J, E connects to L.) Intersect CJ with EL to get F, and intersect DK with BL to get G. Show that FG || JK.

## Cramped space

A triangle with three circles, two of which are tangent. Prove that the upper vertex and the two tangent points are collinear.