# 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. The geometric mean theorem is a special case of the chord theorem.

#### Number of problems found: 48

• Area of RT
The right triangle has orthogonal projections of legs to the hypotenuse lengths 15 cm and 9 cm. Determine the area of ​​this triangle.
• Euclid2
In the right triangle ABC with a right angle at C is given side a=29 and height v=17. Calculate the perimeter of the triangle.
• Euclid3
Calculate height and sides of the right triangle, if one leg is a = 81 cm and section of hypotenuse adjacent to the second leg cb = 39 cm.
• Euclid1
Right triangle has hypotenuse c = 27 cm. How large sections cuts height hc=3 cm on the hypotenuse c?
• Tangents
To circle with a radius of 41 cm from the point R guided two tangents. The distance of both points of contact is 16 cm. Calculate the distance from point R and circle centre.
• RT - hypotenuse and altitude
Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments?
• Triangle ABC
Right triangle ABC with right angle at the C, |BC|=18, |AB|=33. Calculate the height of the triangle hAB to the side AB.
• Circle in rhombus
In the rhombus is an inscribed circle. Contact points of touch divide the sides to parts of length 19 cm and 6 cm. Calculate the circle area.

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