A geometry question about tangent line and two circles.
Circles' whose centers are O_1 and O_2 touch in a point M. AB - O_1 and O_2 tangent line (the same one for both). A and B denotes points where tangent line touches the circles. O_1A = 8 cm, O_2B = 6 cm. Find AB.

Question

A geometry question about tangent line and two circles.
Circles' whose centers are O_1 and O_2 touch in a point M.  AB - O_1 and O_2 tangent line (the same one for both). A and B denotes points where tangent line touches the circles. O_1A = 8 cm, O_2B = 6 cm. Find AB.

zyberg · Answer

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zyberg · Answer

(Both of the circles are as well tangent to each other)

sachintha · Answer

You need to find the coordinates of points A and B.

zyberg · Answer

So, I would have to draw a coordinate plane and then find the coordinates of A and B (Any way to do that without drawing the circles?), then I would solve for length between A and B?
Are there no other ways to solve this?

sshayer · Answer

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sshayer · Answer

Here draw O2C || AB
then apply pythagoras's theorem.

sachintha · Answer

Perfect!

zyberg · Answer

@sshayer Thank you very much! :)

sshayer · Answer

yw