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Category Archives: Geometry
3 squares; (b/x)^2 – (a/x)^2 = (c/x)^2 – (b/x)^2 = k
. . . geometry is the art of reasoning well from badly drawn figures; however, these figures, if they are not to deceive us, must satisfy certain conditions; the proportions may be grossly altered, but the relative positions of the … Continue reading
Angles in a Triangle: 55, 15 and 110
In a triangle, the angles opposite to sides a, b, c measure 55, 15 and 110, respectively. Can you prove that c^2 – a^2 = ab ? … Continue reading
Area between three tangent circles?
3 circles of radius r such that all three are externally tangent, what is the area of the shape in the center in terms of r? What’s the area between three tangent circles? Area … Continue reading
Rectangle, Isosceles Triangle Inscribed In a Circle
Inscribe a rectangle of base W and height H and an isosceles triangle of base W in a circle of radius one as shown. For what value of H do the rectangle and triangle have the same area? … Continue reading
