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Three Balls

A circle has centre O and angle POR = angle QOR. Construct tangents at P and Q meeting at T. Draw a circle with diameter OT. Do P and Q lie inside, or on, or outside this circle?

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The centre of the larger circle is at the midpoint of one side of an equilateral triangle and the circle touches the other two sides of the triangle. A smaller circle touches the larger circle and two sides of the triangle. If the small circle has radius 1 unit find the radius of the larger circle.

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The Eyeball Theorem

Two tangents are drawn to the other circle from the centres of a pair of circles. What can you say about the chords cut off by these tangents. Be patient - this problem may be slow to load.

Some(?) of the Parts

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

A circle touches the lines $OA$ extended, $OB$ extended and $AB$ where $OA$ and $OB$ are perpendicular.

Show that the diameter of the circle is equal to the perimeter of the triangle.