It is known that the lengths of three sides of a triangle are 4cm, 5cm and 6cm respectively. The three circles centered on each vertex are tangent to each other, and the radii of the three circles are calculated most urgent

It is known that the lengths of three sides of a triangle are 4cm, 5cm and 6cm respectively. The three circles centered on each vertex are tangent to each other, and the radii of the three circles are calculated most urgent

Let the radii of three circles be x, y and Z respectively
Then x + y = 4
y+z=5
x+z=6
The three formulas are added and simplified to get x + y + Z = 7.5
So z = 3.5
x=2.5
y=1.5

The lengths of the three sides of the triangle are 5cm, 12cm and 13cm respectively. If the three circles centered on the three vertices of the triangle are circumscribed, the radii of the three circles are______ ．

Let the radii of the three circles be xcm, YCM and ZCM respectively. Since the lengths of the three sides of the triangle are 5cm, 12cm and 13cm respectively, we can get the three circumscribed circles whose three vertices are the center of the triangle. Then we can easily get the following equation: x + y = 5, ① y + Z = 12, ② Z + x = 13, ③ - ② x-z = - 7, ④, ③ + ④ 2x = 6, and the solution is: x = 3, substituting x = 3 into ① y = 2, substituting y = 2 into ② z = 10, The solution is: x = 3Y = 2Z = 10. So the answer is: 3cm, 2cm, 10cm

Take the three vertices of a triangle whose sides are 3cm, 4cm and 5cm as the center of the circle and make the circle tangent to the opposite side respectively. What are the radii of the three circles?

The radii are 3 cm, 4 cm and 3 × 4 / 5 = 2.4 cm respectively