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If two tangent segments to a circle share a common endpoint outside the circle, then the two segments are congruent.
G
We are given a diagram and asked to find the perimeter of △ RST.
If two tangent segments to a circle share a common endpoint outside the circle, then the two segments are congruent. Let's find these segments in our figure.
From the previous figure, we can deduce that x+1 and 5 are equal. With this information, we can write and solve an equation for x. x+1= 5 ⇔ x=4 We can substitute x=4 and find the lengths of all the segments written in terms of x.
| Length | Substitute | Simplify |
|---|---|---|
| x+1 | 4+1 | 5 |
| 3x-2 | 3* 4 - 2 | 10 |
| x-1 | 4-1 | 3 |
Let's draw the length of the segments in the figure.
Finally, we can find the perimeter of the triangle by adding all the side lengths. P&= 5+ 5+ 10+ 10+ 3+ 3 P&= 36 Therefore, the perimeter of △ RST is 36 units. This corresponds to option G.