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Re: If a circle circumscribes a triangle bounded by the x-axis, y-axis and
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31 Mar 2020, 02:00

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If a circle circumscribes a triangle bounded by the x-axis, y-axis and the line 3y - 4x = -24, what is the radius of the circle ?

A. 2.5 B. 3 C. 4 D. 5 E. 10

Since the triangle is bounded by both axes origin (0,0) is one of the vertices of the triangle. At x-axis, y = 0, For 3y - 4x = -24, x = 6 So another of the vertices of the triangle is point (6,0)

At y-axis, x = 0 For 3y - 4x = -24, y = -8 So third of vertices of the triangle is point (0,-8)

So, the triangle is a right angled triangle at origin (0,0) with side lengths 6(x-axis) and 8(y-axis).

As circle is circumscribing the triangle, the hypotenuse is the diameter of the triangle. Hypotenuse = \(\sqrt{6^2 + 8^2}\) = 10

Radius of circle = \(\frac{Hypotenuse of triangle }{ 2} = \frac{10}{2}\) = 5

Answer D.
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Re: If a circle circumscribes a triangle bounded by the x-axis, y-axis and
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31 Mar 2020, 02:00

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The intercepts of the line 3y - 4x = -24 are (0,-8), (6,0). Hence the lengths of the sides of the triangle are 6,8, and 10. Radius of a circle that circumscribes the triangle of side 6,8,10 = 6*8*10/(4A) where A is the area of the triangle = 6*8/2 = 24 Radius = 480/96 = 5.

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31 Mar 2020, 02:05

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Note: The hypotenuse is the diameter of the circle [Angle inside a semicircle is 90 degrees]

For the line 3y - 4x = -24, To find x-intercept: Put y = 0; --> -4x = -24 --> x = 6

To find y-intercept: Put x = 0; --> 3y = -24 --> y = -8

So, the opposite ends of the diameter are (6, 0) & (0, -8) --> Diameter = \(\sqrt{(6 - 0)^2 + (0 - (-8))^2} = \sqrt{100} = 10\) --> Radius of the circle = 10/2 = 5

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31 Mar 2020, 04:48

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If a circle circumscribes a right angle triangle then the longest side (hypotenuse) is the diameter of the circle. Here the sides are 6,8 and 10 (considering the positive distances) X intercept is 6 Y intercept is -8 So diameter=10, radius = 5 D is the answer

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31 Mar 2020, 12:32

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Quote:

If a circle circumscribes a triangle bounded by the x-axis, y-axis and the line 3y - 4x = -24, what is the radius of the circle ?

A. 2.5 B. 3 C. 4 D. 5 E. 10

3y-4x=-24, 3y=4x-24, y=4/3(x)-8 y=0: 4x/3=8, x=3*8/4=6 x=0: y=-8 right triangle sides 8 and 6 hypotenuse: 8^2+6^2=64+36=100^(1/2)=10 rule: for any right triangle, the hypotenuse is a diameter of the circumcircle d=10, r=5

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31 Mar 2020, 14:49

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3y - 4x = 24 --> 3y=4x-24 --> y=4x/3-8 intersection point with y-axis (x=0) --> y=8 intersection point with x-axis (y=0) --> x=6 The triangle is a right triangle with sides 6 and 8 --> the hypotenuse of the right triangle is the diamater of the circle Diameter= (8^2+6^2)^(1/2)=10 Radius=Diameter/2=5 --> Hence D

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31 Mar 2020, 20:45

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The circle will be formed with intercept on x axis as 6,0 and y axis as 0,-8 since x and y axis are perpendicular to each other the hypotenuse will be \(\sqrt{ 6^2 +8^2}\) = 10 Also since the axis are perpendicular to each other hypotenuse is the diameter of a circle = 10 hence radius = 5 cm = D

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31 Mar 2020, 21:26

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If a circle circumscribes a triangle bounded by the x-axis, y-axis and the line 3y - 4x = -24, what is the radius of the circle ?

if x= 0, then y = —8 (0,—8) if y= 0, then x = 6 (6, 0) —> the triangle should be right-angled triangle. Its hypotenuse is 10. —> The hypotenuse of any right-angled triangle inscribed in the circle must be diameter of that circle. —> R = 10/2 = 5

Answer (D)

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31 Mar 2020, 21:26