# The right triangle altitude theorem - math problems

The altitude to the hypotenuse is the geometric mean of the two segments of the hypotenuse. Each leg of the right triangle is the mean proportional of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.$h=\sqrt{{c}_{1}{c}_{2}}$

Also known as a geometric mean theorem. Geometric mean theorem is a special case of the chord theorem.

#### Number of problems found: 46

- Rhombus

It is given a rhombus of side length a = 19 cm. Touchpoints of inscribed circle divided his sides into sections a_{1}= 5 cm and a_{2}= 14 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus. - Rhombus and inscribed circle

It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals. - Paratrooper

After the parachute is opened, the paratrooper drops to the ground at a constant speed of 2 m/s, with the sidewinding at a steady speed of 1.5 m/s. Find: a) the magnitude of its resulting velocity concerning the ground, b) the distance of his land from a - Squares above sides

Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm^{2}. The height vc to the side AB is 3 cm long. The heel P of height vc divides the AB side in a 2: 1 ratio. The AC side is longer than the BC side. Calc - The bomber

From what distance in front of the target must a parachute load be dropped from an aircraft flying at an altitude of 1260 m if it slopes at a speed of 5.6 m/s and at the same time is carried in the direction of movement at a speed of 12 m/s. What is the d - Goat and circles

What is the radius of a circle centered on the other circle and the intersection of the two circles is equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which g

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