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# Two perpendicular chords with lengths 12.2 cm and 8.8 cm have a common endpoint.What is the area of the circle?

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Two perpendicular chords with lengths 12.2 cm and 8.8 cm have a common endpoint.What is the area of the circle?

May 5, 2014

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Here's a graph (drawn to scale) to illustrate Chris's answer:

May 5, 2014

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10736

May 5, 2014
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Two perpendicular chords with lengths 12.2 cm and 8.8 cm have a common endpoint.What is the area of the circle?

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If the chords are perpendicular, they form a right angle, and in a circle, an inscribed angle measures 1/2 of its intercepted arc. So, the arc it intercepts is a half-circle. Thus the remaining side of this right triangle (the hypoteneuse) is a diameter.

So (12.22 + 8.82)(1/2)  ≈ 15.04 cm   And half of this is the raius of the circle = 7.52

And the area of the circle is pi*(7.52)2  ≈ 177.66cm2

May 5, 2014
#3
+27336
+11

Here's a graph (drawn to scale) to illustrate Chris's answer:

Alan May 5, 2014
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Nice, Alan !!!

Thumbs UP !!

May 5, 2014
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Thanks forthe answer Chris,  I had my eye on that one but you beat me to it. haha

Yes, great picture Alan.   I am going to try to reproduce it, did you draw it in GeoGebra or in one of your other programs?

I just realised how i would do it.  I'd use the xy axes for the right angle and then it should be easy.

Does anyone now how to use GeoGebra well?  It is not very intuitive!  I think you are supposed to be able to turn your diagrams into LaTex code in there as well.

I am sure it is brilliant if you can ever learn how to use it properly!

May 6, 2014