Question

The segments in each figure are tangent to the circle at the points shown.
Find each length.

Answer 1

y = 12

Explanation:

The segments are equal in length, SR = TR, so set up an equation:

`(y^2)/(12)=y`

Multiply by 12.

`y^2=12y\\y^2-12y=0`

Factor out the y on the left side.

`y(y-12)=0`

There are two solutions: y = 0 and y = 12. The y = 0 solution makes no sence (segment SR can't have a length of 0). The other solution, y = 12, works just fine.