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You are not logged in. #2 20060408 14:52:50
Re: Radius given arc length and central riseThe length of an arc of a circle is given by the formula where r is the raidus of the circle. But the question gives us only the distance from the centre of the chord to the centre of the arc. Let this length be l. Lets assume the arc is formed by the two radii with an angle θ. Let the distance from the centre of the circle to centre of the chord be x. Let the arc cut the circle at points X and Y and O be the Centre. Let the Centre of the chord be M and centre of the Arc be N. MN=l, OM=x, ON=OM+ON = l+x But ON=r, therefore, l+x=r. An isoceles traingle XOY is formed. The length of the chord is given by the formula . In triangle OMX, OX=r, OM=x=rl and From this the radius can be found (I guess ) Character is who you are when no one is looking. #4 20060408 20:33:48
Re: Radius given arc length and central risegsandy, The arc length is given in the problem. The other equation is (By Pythagoras theorem) where l is the distance from centre of chord to centre of arch. This is given in the problem. Character is who you are when no one is looking. #5 20060409 03:18:32
Re: Radius given arc length and central riseWhile we're on the subject, I derived a cool formula to find the radius of a circle when the length and height of the chord are found. Like so: Last edited by mikau (20060409 03:31:47) A logarithm is just a misspelled algorithm. 