Solve for x. Round your answer to the nearest tenth.
2 answers:
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Answer:
See Below.
Step-by-step explanation:
Please refer to the diagram below.
We are given that O is the center of the circle, and chords MN and RS are intersected a P. OP is the bisector of ∠MPR. And we want to prove that MN = RS.
We will construct segments OK and OJ such that it perpendicularly bisects MN and RS.
Since OP bisects ∠MPR, it follows that:
And since OK and OJ are perpendicular bisectors:
Therefore:
By the Reflexive Property:
Therefore:
By AAS Congruence.
Hence:
By CPCTC.
Recall that congruent chords are equidistant from the center.
Thus, by converse, chords that are equidistant from the center are congruent.
Therefore:
