A triangle ABC is written in a circle, one of the sides of which is the diameter of the circle.

| May 9, 2021 | education

A triangle ABC is written in a circle, one of the sides of which is the diameter of the circle. AB = 15, BC = 9. Find the length of the AC triangle and the P / S triangle.

According to the condition, one of the sides of the inscribed triangle is the diameter of the circle, then the angle ABC of the triangle is based on the diameter of the circle, and therefore is equal to 90. Then the triangle ABC is rectangular, and by the Pythagorean theorem we determine the length of the hypotenuse AB.

AC ^ 2 = AB ^ 2 – BC ^ 2 = 15 ^ 2 – 9 ^ 2 = 225 – 81 = 144.

AC = 12 cm.

Then the perimeter of the triangle is:

P = AB + BC + AC = 15 + 9 + 12 = 36 cm.

Determine the area of the triangle:

S = AC * BC / 2 = 12 * 9/2 = 54 cm2.

Then P / S = 36/54 = 2/3.

Answer: AC = 12 cm, P = 36 cm, S = 54 cm2, P / S = 2/3.



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