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The radius of a circle is 34 meters long, and the chord of the circle is 60 meters long. How far is the chord from the center of the circle? (Im very hopeless...please send step by step instructions)

Kaitlin020

by Kaitlin020 at January 04, 2011

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Kaitlin -Simply draw a sketch of your problem on paper.  Draw a chord AB (see my picture) and the chord has length 60 as stated in the problem or half the chord AC is length 30, agree?Now draw a line from the center of the circle O to A.  The length OA equals the radius of 34, agree?Triangle OAC is a right triangle and if you know the length of OA = 34 and AC = 30, so use the Pythagorean Theorem to solve for OC the distance the chord is from the center of the circle:(AC)^2 + (OC)^2 = (OA)^2Now just plug in the numbers and solve for OCHope this helps

Steve204 Steve204 January 04, 2011

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okay think of it as a triangle with the chord of 60 meters as the base of the triangle extend 2 line from center to endpoint of chord to form a triangle. since the line goes from the center to the endpoint it is the radius and thus is 34. we have just formed a triangle. now draw a perpendicular line from center to base of triangle to for two right triangles, a theorem lets you divide the base in 2 equal lengths so each right triangles has a leg measure of 30. now we have two sides of a right triangle the hypotenuse(34) and one leg of 30. now use pythagorean to find the missing length i.e the distance to the chord from the center which is what you are trying to find.

GURUKID GURUKID January 06, 2011

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