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PS Geometry

by sud21 » Sat Sep 19, 2015 5:14 am
Circle J is centered on the origin. If the equation for a chord within that circle is x+3 √ y=5 and that chord intersects the circle at the x -axis, what is the circumference of Circle J?

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by [email protected] » Sat Sep 19, 2015 10:23 am
Hi sud21,

While this prompt 'looks' complex, it's actually a 'gettable' question IF you recognize the point that the chord intercepts...

We're told that the circle is CENTERED at the ORIGIN (so the circle is symmetric around the Origin) and that the chord in question intersects the circle at the X-axis.

When a point is on the X-axis, it's Y-co-ordinate is 0. Thus, since the equation of the chord is....

x+3√y=5

X + 0 = 5

X = 5

The X-intercept of the end-point on that chord is 5. Since the circle is symmetric around the Origin, the radius of the circle is 5. The formula for Circumference of a circle is...

Circumference = 2(pi)(radius) = 2(pi)(5) = 10pi

Final Answer: E

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