Question

If RS=59 AND ST=10x-31,find x

Answer 1

Answer: x=9

Step-by-step explanation:

In the given picture, we have a circle in which we have given two congruent arcs $\overarc{RS}\text{ and }\overarc{TS}$

And $\overline{RS}=59\text{ and }\overline{ST}=10x-31$

Since, we know that congruent arcs have congruent chords.

Therefore,  $\overline{RS}=\overline{ST}$

$59=10x-31\\\\\Rightarrow\ 10x=59+31\\\\\Rightarrow 10x=90\\\\\Rightarrow x=\frac{90}{10}\\\\\Rightarrow x=9$

Answer 2

To solve the problem we must know the Chord's Equidistant From The Center Of A Circle Theorem.

Equidistance chords

If two chords of a circle are equidistant from the center then they are congruent to each other and their corresponding arcs are also congruent.

The value of x is 9.

Given to us

• RS = 59,
• ST = 10x-31,

In circle,

Chord RS and chord ST are equidistant from the center. therefore,

RS = ST

$59 = 10x-31\\ 59+31 = 10x\\ 90 = 10x\\\\ x= \dfrac{90}{10}\\\\ x= 9$

Hence, the value of x is 9.

Learn more about Equidistance chords:

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