It is known that the lengths of the three sides of △ ABC are 10cm and 11cm.13cm respectively, and ⊙ a. ⊙ B. ⊙ with the three vertices of the triangle as the center C is tangent to each other to find the radius of three circles

Let three radii a, B, C,
Then a + B = 10, a + C = 13, C + B = 11
a=6,b=4,c=7

The sides of a regular triangular pyramid are right triangles, and the length of the bottom side is a. find its area

The sides of a regular triangular pyramid are right triangles, which should be isosceles right triangles with hypotenuse at the bottom
Bottom area: 1 / 2 * a * radical 3 / 2 * a = radical 3 / 4 * A & #
Side area: 1 / 2 * a * 1 / 2A * 3 = 3 / 4A & #

If the sides of a regular triangular pyramid are all right triangles and the bottom side is 2a, then its side area is

S side = 1 / 2 * D * h * 3
=0.5*2a*a*3
=a*a*3
=3a^2

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