Question

A chain fits tightly around two gears as shown. What is the radius of the smaller gear? Round your answer to the nearest tenth.

Answer 1

Using the Pythagorean theorem we can solve for the radius

see attached picture: 

Answer 2

Answer:

The correct option is 3.

Step-by-step explanation:

From the given figure it is noticed that the radius of a circle is 11 inches and the centers of two circles are 20 inches apart. The length of the direct common tangent between both circles is 19 inches.

If the centers of two circles of radius r₁ and r₂ are d units apart, then the length of the direct common tangent between them is

$l=\sqrt{d^{2}-(r_{1}-r_{2})^{2}}$

$19=\sqrt{20^{2}-(11-r_{2})^{2}}$

Square both sides.

$361=400-(11-r_{2})^{2}$

$(11-r_{2})^{2}=400-361$

$(11-r_{2})^{2}=39$

Tnking square root both sides.

$11-r=\sqrt{39}$

$11-6.245=r$

$4.775=r$

$r\approx 4.8$

Therefore the radius of second circle is 4.8 inches and option 3 is correct.