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Two semicircle sit on the diameter of a semicircle centre O of twice their radius. Lines through O divide the perimeter into two parts. What can you say about the lengths of these two parts?

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Set Square

A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?

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Strange Rectangle

ABCD is a rectangle and P, Q, R and S are moveable points on the edges dividing the edges in certain ratios. Strangely PQRS is always a cyclic quadrilateral and you can find the angles.

Fixing It

Stage: 5 Challenge Level: Challenge Level:1

$A$ and $B$ are two fixed points on a circle and $RS$ is a variable diamater. What is the locus of the intersection $P$ of $AR$ and $BS$?