3-4-5 Triangle

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

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

From the figure shown, AB = diameter of circle O1 = 30 cm, BC = diameter of circle O2 = 40 cm, and AC = diameter of circle O3 = 50 cm. Find the shaded areas A1, A2, A3, and A4 and check that A1 + A2 + A3 = A4 as stated in the previous problem.

Circles with centers at midpoints of sides of a right triangle


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