Question

Катети прямокутного трикутника дорiвнюють 6 i 8 см.Знайдiть радiус кола вписаний в цей трикутник

Answer 1

По т. Пифагора находим гипотенузу
с² = a² + b² = 36 + 64 = 100
c = √100 = 10. 
Радиус вписанной окружности по формуле
$r= \sqrt{ \frac{(p-a)(p-b)(p-c)}{p} }$
p = (a+b+c)/2 = 12.
p-a = 6
p-b = 4
p-c = 2
r = 2 - ОТВЕТ
Рисунок - в приложении.

Answer 2

Finding the Radius of the Inscribed Circle

To find the radius of the inscribed circle in a right-angled triangle with the given side lengths, we can use the formula:

radius = (a + b - c) / 2

Where: - a and b are the lengths of the legs of the right-angled triangle - c is the length of the hypotenuse

In this case, the lengths of the legs are 6 cm and 8 cm.

Calculation

Using the formula, we can calculate the radius of the inscribed circle:

radius = (6 + 8 - 10) / 2 radius = 4 / 2 radius = 2 cm

So, the radius of the inscribed circle in the given right-angled triangle is 2 cm.