Stage: 5 Challenge Level: 
 |
Two semi-circles are drawn on one side of a line
segment. Another semi-circle touches them externally as
shown in the diagram.
What is the radius of the circle that touches all three
semi-circles?
|
Radius (radii) & diameters. Cosine rule. Surds. Manipulating algebraic expressions/formulae. Creating expressions/formulae. Circles. Pythagoras' theorem. Long problems. Mathematical reasoning & proof. Quadratic equations.
Published November 1999.
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