   SEARCH HOME Math Central Quandaries & Queries  Question from erson, a student: this is the last..... please help me i humbly request.....if possible....may i get the answer tomorrow... because i'll be needing this the day after tomorrow... find the length of the tangent segment AB to two circles whose radii are a and b respectively, when the circles touch each other. the illustration looks like this...hope you'll understand... there are 2 circles - one is big one is small. they touch each other. and there is this irregular 4 sided polygon that connects them...there is a line that connects them from their center point and another from the tip of the circles...and that's it...i cannot explain very well please bear with me I think you are looking at this diagram: Remember that radii meet points of tangency at right angles, so that means the two radii drawn are parallel to each other. Now if I draw a blue line parallel to the tangent line here: Then I have created a rectangle. Therefore the length of the blue line is the same as the length x you are trying to find. As well, you know the lengths of two of the sides of the triangle you see there and can show that it is a right triangle: Solve for x.

Cheers,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.