In a right-angled triangle ABC with a right angle c, the coordinates are known

| August 5, 2021 | education

In a right-angled triangle ABC with a right angle c, the coordinates are known: AC = 6 BC = 8 find the radius of the circle of the written off triangle ABC.

Knowing the lengths of the legs of a right-angled triangle ABC, we determine the length of the hypotenuse AB by the Pythagorean theorem.

AB ^ 2 = BC ^ 2 + AC ^ 2 = 64 + 36 = 100.

AB = 10 cm.

Through the lengths of the sides of a right-angled triangle, we determine the radius of the inscribed circle.

R = OH = (BC + AC – AB) / 2 = (8 + 6 – 10) / 2 = 2 cm.

Second way.

Determine the area of the triangle ABC.

Savs = BC * AC / 2 = 8 * 6/2 = 24 cm2.

Let us determine the length of the hypotenuse AB.

AB ^ 2 = BC ^ 2 + AC ^ 2 = 64 + 36 = 100.

AB = 10 cm.

The semi-perimeter of the triangle ABC is equal to: p = (AB + BC + AC) / 2 = (10 + 8 + 6) / 2 = 12 cm.

Then R = OH = Savs / p = 24/12 = 2 cm.

Answer: The radius of the circle is 2 cm.



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