Question

M is the midpoint of PQ. The diameter of a circle O is 13 in. And RM = 4 in.

Answer 1

Part a)
`PM=6\ in`

Part b)
`PQ=12\ in`

Explanation:

step 1

we know that

The diameter of the circle divide the circle into two equal parts

so

PM=MQ

Applying the Intersecting Chord Theorem (When two chords intersect each other inside a circle, the products of their segments are equal)

`SM*RM=PM*MQ`

`SM*RM=PM^(2)`

we have

`SM=13-4=9\ in`

`RM=4\ in`

substitute

`9*4=PM^(2)`

`PM^(2)=36`

`PM=6\ in`

step 2

Find the value of PQ

we know that

`PM=MQ`

so

`PQ=PM+MQ`

`PQ=2PM`

we have

`PM=6\ in`

substitute

`PQ=2(6)=12\ in`