Question

Find the length of the following tangent segments to the circles centered at O and O's whose radii are 5 and 3 respectively and the distance between O and O's is 12. Find segment AB

Answer 1

AB = 2 sqrt(35) (or 11.83 to two decimal places)

Explanation:

Refer to diagram.

ABO'P is a rectangle (all angles 90)

=>

PO' = AB

AB = PO' = sqrt(12^2-2^2) = sqrt(144-4) = sqrt(140) = 2sqrt(35)

using Pythagoras theorem.