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Two semicircles are drawn on one side of a line segment. Another semicircle touches them externally as shown in the diagram.
What is the radius of the circle that touches all three semicircles in terms of the radii of the first two semicircles?

Four rods are hinged at their ends to form a quadrilateral. How can you maximise its area?
P is a point inside a square ABCD such that PA= 1, PB = 2 and PC = 3. How big is angle APB ?
Rearrange the pieces of the puzzle to form a rectangle and then to form an equilateral triangle. Calculate the angles and lengths.