A circle is inscribed in a right-angled triangle. The point of contact with the hypotenuse

| January 31, 2021 | education

A circle is inscribed in a right-angled triangle. The point of contact with the hypotenuse divides it into parts equal to 6cm and 4cm find the radius of the circle.

By the property of tangents drawn from one point, their lengths are equal, then: ВK = BH = 6 cm, AM = AH = 4 cm.

The radii OK and OM drawn to the points of contact are perpendicular to them, then the quadrangle is OKCM square, with a side equal to the radius of the circle. CM = СK = R.

Then BC = (6 + R), AC = (4 + R).

Then, by the Pythagorean theorem: AB ^ 2 = BC ^ 2 + AC ^ 2.

100 = (6 + R) ^ 2 + (4 + R) ^ 2 = 36 + 12 * R + R ^ 2 + 16 + 8 * R + R ^ 2.

2 * R ^ 2 + 20 * R – 48 = 0.

R ^ 2 + 10 * R – 24 = 0

Let’s solve the quadratic equation.

R1 = -12 cm. (Not suitable as less than 0).

R2 = 2 cm.

Answer: The radius of the circle is 2 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.