Question

СРОЧНО!!!Окружность проходит через вершину прямого угла C и пересекает его стороны в точках A и B. Найдите радиус окружности, если AC=6, BC=8. Варианты ответов: 1-4, 2-5, 3-6, 4-8, 5- нельзя опредилить... С РЕШЕНИЕМ ПОЖАЛУЙСТА!!!

Answer 1

Решение на фото ниже

Answer 2

Problem Analysis

We are given that a circle passes through the vertex of a right angle C and intersects its sides at points A and B. We need to find the radius of the circle given that AC = 6 and BC = 8.

Solution

To find the radius of the circle, we can use the property that the perpendicular from the center of a circle to a chord bisects the chord. In this case, the chord AB is bisected by the perpendicular from the center of the circle.

Let O be the center of the circle. Since the perpendicular from O bisects AB, we can find the length of OB by using the Pythagorean theorem on the right triangle OCB. Similarly, we can find the length of OA by using the Pythagorean theorem on the right triangle OCA.

Let's calculate the lengths of OB and OA:

- OB: Using the Pythagorean theorem on triangle OCB, we have OB^2 = OC^2 - BC^2. Substituting the given values, we get OB^2 = r^2 - 8^2.

- OA: Using the Pythagorean theorem on triangle OCA, we have OA^2 = OC^2 - AC^2. Substituting the given values, we get OA^2 = r^2 - 6^2.

Since the perpendicular from O bisects AB, we have OB = OA. Therefore, we can equate the expressions for OB^2 and OA^2:

r^2 - 8^2 = r^2 - 6^2

Simplifying the equation, we get:

64 = 36

This is not a valid equation, as it leads to a contradiction. Therefore, it is not possible to determine the radius of the circle given the lengths of AC and BC.

Answer: 5- нельзя определить