# Monthly Archives: October 2016

## tan A = tan B + tan C + tan D

Find other   4-tuples     of distinct integers between     and     that satisfy the relation   Other solutions:     How many such equations can you produce if we allow repeated angles?   … Continue reading

Posted in Number Puzzles | | 4 Comments

Establish the following For any triangle   ,     and where     is the circumradius,     the inradius and     the semiperimeter. Then     are in geometric progression iff           … Continue reading

Establish the following For any triangle   ,     and where     is the circumradius,     the inradius and     the semiperimeter. Then     are in arithmetic progression iff           … Continue reading

## Pythagorean triple(a,b,c); integer solutions of the equation a^2 + ab + b^2

The integers form a Pythagorean triple. There are similar formulas for integer solutions of the equation   It can be verified that satisfy the equation   If   x   and   y   are integers, then   … Continue reading

## 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

Posted in Geometry | Tagged | 3 Comments

## Primitive Pythagorean triples- radius of incircle is a square

The radius of incircle is a square   –   up to the value of                                               … Continue reading

Posted in Number Puzzles | | 1 Comment

## Set of 3 Pythagorean triangles equal perimeters and area in A.P.

Here are sets of 3 Pythagorean triangles with equal perimeters and area in arithmetic progression. Note that the perimeters are multiples of 120.      The pattern breaks in this example: The perimeter is not a multiple of … Continue reading

Posted in Number Puzzles | | 2 Comments

## Part 2 – PT diff. between sides,perim,diam. of inscribed circles are squares,diff. between Areas a cube

Part 1 – Pythagorean triangles diff. between sides,perim,diam. of inscribed circles are squares,diff. between Areas a cube Find two Pythagorean triangles     and     such that are all squares And, the difference of areas a cube … Continue reading