# Category Archives: Geometry

## Right triangle in a rectangle

An infinite number of rectangles may be generated, each with a right triangle inscribed as shown:     such that the lengths of the sides of the various right triangles are integers.                                 *****************************************                   … Continue reading

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## What are the proportions of the areas of the rhombuses?

A circle is divided into twelve equal arcs, and the points of division are joined as shown here:     What are the proportions of the areas of the rhombuses formed ?             … Continue reading

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## Splitting the hypotenuse into 3 segments

In   (Fig. 1) ACB is a right triangle CD = m,     CE = n AD = DE = EB = x AB = c   Prove that        In   (Fig. 2) Under what condition(s) … Continue reading

## tan in G.P. and cot in A.P.

In a triangle ADC,   AD = AC   and   AE   is the altitude CD is extended to point B such that   BA = 10

## Crescent shape

C is the centre of the larger circle. What are the diameters of the two circles?     Lune (mathematics) http://en.wikipedia.org/wiki/Lune_(mathematics)   Answer:   Explain this result.                         … Continue reading

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## Two concentric circles

We have two concentric circles. Radius for the big circle     is R Radius for the smaller circle     is r The chord of     which is tangent on the inner circle has a known length. … Continue reading

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## Equilateral triangle inscribed in a rectangle

An equilateral triangle ABC is inscribed in a rectangle. If   X,   Y,   Z   are the areas of the complementary right triangles. Prove that                    X   +   Y   =   Z   … Continue reading

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## Dividing an L-shape figure into 4 equal figures

Solution : Each figure is contiguous and is identical in shape and size to the other.   Same question with a 3/4 of a circle   Estimating the area of a heart shape:                         … Continue reading