A circle 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.
1 answer:
Answer:
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
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Answer:
C
Step-by-step explanation:
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So now we put them all together And if you look, C matches that exactly.
Answer:
Step-by-step explanation:
If a point (x, y) lies on a straight line, coordinates of the point will satisfy the equation.
Slope of a line passing through two points C(4, 5) and D(8, 10),
m =
m =
m =
Equation of the line passing through C(4, 5) and slope m =
y - y' = m(x - x')
y - 5 =
y =
y =
If point B(4, 0) lies on the line CD,
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Which is not true.
Therefore, point B doesn't lie on line CD.