Question

⊙M≅⊙N and AB=31.8. Identify PQ, rounded to the nearest tenth.

Answer 1

`PQ=9.6\ units`

Explanation:

In this problem

If AB=31.8 units

then

ZY=31.8 units

ZP=PY=31.8/2=15.9 units

In the right triangle MZP

we have

`ZP=15.9\ units`

`MZ=18\ units` ----> the radius of the circle

Applying Pythagoras Theorem Find MP

`MP^(2)=MZ^(2)-ZP^(2)`

substitute

`MP^(2)=18^(2)-15.9^(2)`

`MP^(2)=71.19`

`MP=8.4\ units`

Find the value of PQ

we know that

`MQ=MP+PQ\\ PQ=MQ-MP`

we have

`MQ=18\ units`

`MP=8.4\ units`

substitute

`PQ=18-8.4=9.6\ units`