1. ## Included Angle Problem!

I have a question.

If two disk. 1-1/2 inches and 1-7/8 inch in diameter, respectively, are in contact with each other. What is the included angle of two lines that are tangent to both circles.

I am having trouble finding a soloution. Any Ideas? To five decimal places.

I have a question.

If two disk. 1-1/2 inches and 1-7/8 inch in diameter, respectively, are in contact with each other. What is the included angle of two lines that are tangent to both circles.

I am having trouble finding a soloution. Any Ideas? To five decimal places.
The centers of the disks are (1.5+1.875)/2 inches apart (1.6875 inches).

The difference between lengths of the radii is

(1.875-1.5)/2 = 0.1875

From the line, which is tangent to both circles:
The perpendicular distance from the line to the center of the smaller disk is the radius, or 0.75 inches.
The perpendicular distance from the line to the center of the larger disk is the radius, or 0.9375 inches.
We have a triangle:
We know the hypotenuse length (sum of the two radii) and we know then length of the opposite side (0.9375 - 0.75 = 0.1875 )

$\displaystyle ArcSin \left ( \dfrac{0.1875}{1.6875} \right ) = 0.111341$ radians.

That is HALF of the total angle.
You will need to double the above to get the answer sought.