Circle and Chord

[keizer Soze]

Any ideas how to solve this? I couldn´t, don´t know if it´s right.

Circle X has chord AB that intersects radius XC in point D and angle XDB is 90°. If AB=12 and DC=2. What is the circumference of the circle?


[spoiler]20 ∏[/spoiler]

[dumb.doofus]

[keizer Soze]

Thanx doofus!

[4seasoncentre]

kinda hard to explain without a diagram, but.....

We know that XC is the radius. Since the chord intersects at a 90 degree angle, we know that AD=6.

DC=2
Therefore XD = XC -2
note XC is also the radius of the circle, so XD = R - 2
Note that XA is also the radius.

Using Pythagoras:

XD^2 + 6^2 = XA ^2
(r-2)^2 + 36 = r^2
r^2 - 4r + 4 + 36 = r^2

work that out and you get r = 10
Circumference of a circle is defined by
2πr
=2π(10)
=20π

DAMN IT, someone beat me to it!

[PAB2706]

why is the answer different when i take XB=XD+2

[dumb.doofus]

why is the answer different when i take XB=XD+2

It can't be both are equal.. recheck the steps what you are doing.. or post the steps here..