1. ## Circles...

Line BC is tangent to point A at C. If AC = 4 and BA = 5, find BC. Please show how to find this. Thanks!

2. Originally Posted by whytechocolate01
Line BC is tangent to point A at C. If AC = 4 and BA = 5, find BC. Please show how to find this. Thanks!
is point A the center? if so, it forms a right angle when it intersects with the tangent at the circumference. (this is again, the famous 3-4-5 triangle, we know the answer will be 3, but how to find that for certain?)

by Pythagoras' theorem:

(BC)^2 = (AB)^2 - (AC)^2 = 5^2 - 4^2 = 25 - 16 = 9
=> BC = sqrt(9) = 3 ......as expected

if A is not the center, well, i don't know

3. A line can be tangent to a circle. Your problem does not match the figure you sent.
If you consider the context, I would say that A, B ,C are collinear , so BC can be either 9 or 1, depending on the order of the 3 points.

4. Originally Posted by alinailiescu
A line can be tangent to a circle. Your problem does not match the figure you sent.
If you consider the context, I would say that A, B ,C are collinear , so BC can be either 9 or 1, depending on the order of the 3 points.
i thought about that, but i decided to go from the diagram and treat the question as a wierd typo.

5. I think Jhevon is correct

If BC is a tangent to A that means it = 90 degrees
we are given the length of two sides therefore pythagoras theorem can be used

so Jhevon's answer of 3 is correct according to me
maybe you told him to work out the wrong thing?
what's point D for?

6. Originally Posted by Geometor
I think Jhevon is correct

If BC is a tangent to A that means it = 90 degrees
we are given the length of two sides therefore pythagoras theorem can be used
assuming A is the center, which is the reasonable assumption we can make i think

what's point D for?
it's a decoy to confuse you