# 3-4-5 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.