# circle 2

• Dec 1st 2010, 05:06 PM
prasum
circle 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 AM
earboth
Quote:

Originally Posted by prasum
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

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 AM
RTC1996
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 PM
earboth
Quote:

Originally Posted by RTC1996
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?

Sorry for the confusion but in Germany (in Austria and Switzerland also) the number which you write like this

$\displaystyle 12,345.67$

is written like this

$\displaystyle 12.345,67$