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A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle

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Ladder and Cube

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Equilateral Areas

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

ABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF .

Does this work for any whole number side lengths?

If not, under what circumstances does it work?

What if the lengths of the sides of the triangles had been a and b instead of 3 and 4, can you construct an equilateral triangle whose area is the sum of the areas of ABC and DEF ? What is the new area?