Two circles with radii 8 and 5 cm touch each other externally. find length of direct common tangent?

Question

Two circles with radii 8 and 5 cm touch each other externally. find length of direct common tangent

sv could you please explain again how you are getting this expression
SQRT (13^2 - 3^3) = 4*sqrt (10).

Answer 1

With reference to the diagram in the link

OD = 5+8=13cm
OC = 5cm
CD = 12cm (By Pythagoras Theorem - triangle OCD is a right triangle)
Therefore SR = 12cm (CDSR is a rectangle)

Common tangent is 12cm

Answer 2

Gudspeling is correct. And he has a link to a very nice diagram. The only difference is that in the actual problem the two circles are externally tangent. But that just makes it easier to calculate the hypotenuse of the right triangle.

Answer 3

You will have a trapezium with sides R1, R2, R1+R2 and your tangent (the vertexes of the trapezium are the 2 centers of the circles, and the 2 points where the line touches the circles - these two last will have right angles at them).

So - when you "cut" the smaller radius (5) you'll get a right(-angled) triangle with sides 8+5, 8-5, and the one you look for.
So, your tangent will be SQRT (13^2 - 3^3) = 4*sqrt (10).

Answer 4

Cm Touch

Answer 5

um its sqrt (13^2 - 3^2) cuz when you flip the circle you ll see so substracts co which will be 8 - 5 which will give you 3 and then you use pythagorus

Answer 6

Twice the geometric mean of 8 and 5.

Answer 7

DO THE FOLLOWING BY CONSTRUCTING THE CIRCLES ACTUALLY:

> DRAW A LINE WHICH TOUCHES BOTH THE CIRCLES ONLY AT ONE POINT DISTINCT POINT AS TANGENT BUT DON'T DRAW IT AT THE POINT OF CONTACT OF TWO CIRCLES.

> NOW DRAW A PERPENDICULAR AT THE POINT OF CONTACT OF THE LINE WITH THE BIGGER CIRCLE FROM THE RADIUS OF THE CIRCLE WITH RADIUS 8 cm.

> DO THE SAME WITH SECOND SMALLER CIRCLE.

> NOW SIMPLY MEASURE THE LENGHT OF THE TANGENT WITH THE SCALE.

Answer 8

6.5 cm.