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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
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
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
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
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
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
Rectangle, Isosceles Triangle Inscribed In a Circle
Paul says: I get h = 2/5, which makes w = (4 Sqrt[6])/5. The area of both is then (8 Sqrt[6])/25 ~ 0.783837
Fun With Num3ers 