# right triangle

## 01 Minimum distance between projection points on the legs of right triangle

**Problem**

From the right triangle ABC shown below, AB = 40 cm and BC = 30 cm. Points E and F are projections of point D from hypotenuse AC to the perpendicular legs AB and BC, respectively. How far is D from AB so that length EF is minimal?

## 09 Areas outside the overlapping circles indicated as shaded regions

**Problem**

From the figure shown, AB = diameter of circle O_{1} = 30 cm, BC = diameter of circle O_{2} = 40 cm, and AC = diameter of circle O_{3} = 50 cm. Find the shaded areas A_{1}, A_{2}, A_{3}, and A_{4} and check that A_{1} + A_{2} + A_{3} = A_{4} as stated in the previous problem.

## 08 Circles with diameters equal to corresponding sides of the triangle

**Problem**

From the figure shown below, O_{1}, O_{2}, and O_{3} are centers of circles located at the midpoints of the sides of the triangle ABC. The sides of ABC are diameters of the respective circles. Prove that

where A_{1}, A_{2}, A_{3}, and A_{4} are areas in shaded regions.

## 40 - Base angle of a growing right triangle

## 32 - 34 Maxima and minima problems of a rectangle inscribed in a triangle

**Problem 32**

Find the dimension of the largest rectangular building that can be placed on a right-triangular lot, facing one of the perpendicular sides.

## 21 - 24 Solved problems in maxima and minima

**Problem 21**

Find the rectangle of maximum perimeter inscribed in a given circle.

## Functions of a Right Triangle

From the right triangle shown below,

the trigonometric functions of angle θ are defined as follows: