Referring to the attached pic, work out the length of OC - do not use trigonometric ratios stuff if possible.

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- Nov 1st 2009, 12:30 AMukorova question on properties of circle
Referring to the attached pic, work out the length of OC - do not use trigonometric ratios stuff if possible.

- Nov 1st 2009, 12:51 AMOpalg
Draw a tangent to the circle from C, say CT is the tangent and OT is the radius (so the lines CT and OT are perpendicular). There's a theorem which says that $\displaystyle CA\times CB = CT^2$, from which you can find CT. Then use Pythagoras.

- Nov 1st 2009, 01:09 AMukorov
- Nov 1st 2009, 01:20 AMukorov
- Nov 1st 2009, 01:33 AMOpalg
- Nov 1st 2009, 01:49 AMukorov
- Nov 1st 2009, 02:17 AMaidan
Is it considered to be using trigonometric ratios

if you find the mid-point of the chord AB?

Since the chord length is given as 8, half would be 4.

If not then you have two 3-4-5 triangles inside the circle.

You then have sufficient information to complete the sides of a right triangle.

And from there, use pythagoras.

. - Nov 1st 2009, 03:14 AMukorov
- Nov 1st 2009, 05:50 AMOpalg