an isosceles triangle the ratio ri/rc of the inscribed and circumscribed circumference is 1/2. determine the angles of the triangle.​

9514 1404 393

  equilateral triangle: all angles 60°

Step-by-step explanation:

It can be shown easily that an equilateral triangle meets the requirement. It is a little more difficult to show that the requirement forces an equilateral triangle.

In an equilateral triangle, the incenter and the circumcenter are the same point: the centroid. The centroid is half as far from the side as it is from the vertex, so the requirement ri/rc = 1/2 is demonstrated by that property.

the answer is all angles 60°

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb

multiply then divide

step-by-step explanation: