The radius of a circle inscribed in a right-angled triangle is 4, and the hypotenuse is 21.

| June 20, 2021 | education

The radius of a circle inscribed in a right-angled triangle is 4, and the hypotenuse is 21. Find the area and perimeter of the triangle.

Let’s build the radii of the circle OH, OK, OM.

By the property of a tangent drawn from one point, AK = OH, BK = BM, CH = CM.

The radii drawn to the points of contact are perpendicular to the tangents, then AKOH is a square, AK = OK = AH = OH = R = 4 cm.

By the property of tangents drawn from one point: BK = BM, CH = CM.

Ravs = AB + AC + BC = (BK + AK) + (CH + AH) + BC = BK + 4 + CH + 4 + 21 = 29 + (BK + CH) = 29 + 21 = 50 cm.

Then the half-perimeter is equal to: p = 50/2 = 25 cm.

Determine the area of the triangle ABC.

Savs = p * r = 25 * 4 = 100 cm2.

Answer: The perimeter of the triangle is 50 cm, the area is 100 cm2.



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.