if chord y=mx+1 of the circle x^2+y^2=1 subtends an angle 45 degrees at the major segment of the circle,then the value of m is

Printable View

- Dec 1st 2010, 05:06 PMprasumcircle 2
if chord y=mx+1 of the circle x^2+y^2=1 subtends an angle 45 degrees at the major segment of the circle,then the value of m is

- Dec 2nd 2010, 12:59 AMearboth
1. I'm not sure that I understand your question correctly(?).

2. Draw a sketch.

3. The perpendicular bisector of the chord has the slope $\displaystyle n = -\frac1m$ which correspond to an angle of 67.5° to the x-axis.

4. The slope of the sekant correspond to an angle of -22.5° and therefore

$\displaystyle m = \tan(-22.5^\circ)$

5. Use some simple trig-properties to get

$\displaystyle \tan(-22.5^\circ) = 1-\sqrt{2}$ - Dec 2nd 2010, 04:22 AMRTC1996
Why do your angles have commas instead of periods? You wrote 67,5 and 22,5. Shouldn't it be 67.5 degrees and 22.5 degrees?

- Dec 2nd 2010, 01:23 PMearboth