Acircle with radius r is inscribed into a right triangle. find the perimeter of the triangle if: the point of tangency divides the hypotenuse into 5 cm and 12 cm segments.

40 cm

Step-by-step explanation:

If we let r represent the radius of the circle, the legs of the triangle have length 5+r and 12+r. Then the Pythagorean Theorem tells us ...

(5 +12)^2 = (5 +r)^2 +(12 +r)^2

5^2 +2·5·12 +12^2 = 5^2 +2·5·r +r^2 + 12^2 +2·12·r +r^2

120 = 34r +2r^2 . . . . subtract 5^2 +12^2

60 +8.5^2 = 8.5^2 +17r +r^2 . . . . . . divide by 2, add (17/2)^2

11.5 = 8.5 +r . . . . . . . . . . . . . . . . . . . take the square root (negative root is extraneous)

3 = r

The radius of the circle is 3 cm. The perimeter of the triangle is the sum of the side lengths:

(5 +3) cm + (12 +3) cm + (5+12) cm = 2(5 +12 +3) cm = 40 cm

so far i think you have the right thing going for you just remember soh cah toh

step-by-step explanation:

sine over hypotenuse

cosine   equals adjacent

tangent over hypotenuse

the answer is (-8,-5)

step-by-step explanation:

the endpoint to midpoint is half the length. the length is (-2,-1) so when you are at the midpoint just add it to it to find your answer -6+(-2)= -8 and -4+(-1)=-5 so (-8,-5)