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In circle O, CD = 44, OM = 20, ON = 19, CD is perpendicular to OM and EF to ON.
a. Find the radius. If your answer is not an integer, express it in radical form.
b. Find FN. If your answer is not an integer, express it in radical form.
c. Find EF. Express it as a decimal rounded to the nearest tenth.
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OpenSessame
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mathstudent55
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You mean CD is perpendicular to OM and EF to ON, right?
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Yea dont know why i wrote parallel
mathstudent55
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Can you find MD?
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No...
mathstudent55
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|dw:1377142738745:dw|
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Its a right triangle? so can you you the Pythagorean theorem?
mathstudent55
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In the circle above, radius OP is perpendicular to chord AC.
mathstudent55
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Radius OP bisects chord AC, so AB = BC
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|dw:1377142881604:dw|
mathstudent55
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Now look at your figure again.
Notice segment OM and chord CD.
What is the length of MD?
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22?
mathstudent55
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Right. Now draw the radius OD. Since you know two sides of a right triangle, you can find the third side.
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\[\sqrt{884}\]
mathstudent55
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|dw:1377143069512:dw|
mathstudent55
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Correct, but you can simplify it.
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Should I because it says just leave it in radical form...
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I can simplify it myself i know how to do that part lol, but i just need help with the rest!
mathstudent55
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Ok.
Next. What is FN?
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Would that be 22? Because they are perpendicular?
mathstudent55
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|dw:1377143292258:dw|
OpenSessame
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Oh wait no! i get it! dont tell me!!
mathstudent55
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Notice that ON is not the same length as OM, so that side has different dimensions except for the radius which is obviously the same anywhere in the circle.
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\[\sqrt{523}\]
mathstudent55
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Correct. Great job!
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Now EF?
mathstudent55
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Now EF is easy.
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Its just double right?
mathstudent55
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Right, but the write it as a decimal rounded off to the nearest tenth.
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Okay, I got it! Thanks!
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Mind if i tag you for other questions?
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45.7?
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Not at all.
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Thanks:)
mathstudent55
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wlcm