Question

Hewwo!

Answer 1

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:

$\displaystyle \angle JPO\cong \angle KPO$

And since OK and OJ are perpendicular bisectors:

$m\angle OKP=90^\circ \text{ and } m\angle OJP=90^\circ$

Therefore:

$\angle OKP\cong \angle OJP$

By the Reflexive Property:

$OP\cong OP$

Therefore:

$\Delta OKP\cong \Delta OJP$

By AAS Congruence.

Hence:

$OK\cong OJ$

By CPCTC.

Recall that congruent chords are equidistant from the center.

Thus, by converse, chords that are equidistant from the center are congruent.

Therefore:

$MN\cong RS$

Answer 2

Answer:

this is your answer look it once.