A semicircle is inscribed in a right-angled triangle with legs 5 cm and 12 cm and a hypotenuse
July 17, 2021 | education
| A semicircle is inscribed in a right-angled triangle with legs 5 cm and 12 cm and a hypotenuse of 13 cm. Find the radius of the semicircle.
Let us find the radius of the inscribed circle ro by the classical formula:
r = √ (p – a) * (p – b) * (p – c) / p, where a, b, c are sides, p = 1/2 (a + b + c).
P = 1/2 * (5 + 12 + 13) = 10.
r = √5 * (-2) * (-3) / 10 = √25 / 10 = 5 / √10.
Then the required radius is equal to:
2 * 5 / √10 = √10 cm.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.