Question

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

Answer 1

Answer:

Part a) $PM=6\ in$

Part b) $PQ=12\ in$

Step-by-step 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

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