In a right-angled triangle, legs AB and AC are equal to 24 cm and 7 cm

| February 2, 2021 | education

In a right-angled triangle, legs AB and AC are equal to 24 cm and 7 cm, respectively. How many centimeters is the radius of the circumscribed circle around this triangle?

Answer: the radius of the circumscribed circle is 12.5 cm.

Let’s complete the existing triangle to a rectangle by drawing straight lines perpendicular to the legs from the points of intersection of the legs with the hypotenuse. In the resulting rectangle, draw diagonals. The diagonals will divide each other into 2 equal parts, and the point of their intersection will be exactly in the middle of the hypotenuse of the original triangle. It is this point that will be the center of the circumscribed circle. Let us determine the length of the hypotenuse c by the Pythagorean theorem:

24 ^ 2 + 7 ^ 2 = 576 + 49 = 625.

s = √625 = 25 cm.

Determine the radius:

25/2 = 12.5 cm.



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