Question

there are 3 circles, O, N & are all tangent at S. OS is a diameter at circle N. PO is tangent to circle N and PM is a common tangent to circle O and circle Q. The radius of circle Q is 3 and the radius of circle N is 6. Find the length of PM

Answer 1

any questions?

Answer 2

Yes a few. Because of the drawing ( it is not your fault), i am not sure about some things.

Is the point O the center if the circle O?

is POM a right angled triangle?

Answer 3

point O is the center of the biggest circle

Answer 4

help!!!

Answer 5

yea im here. Just need to know if POM is a right angled triangle, that is important i think. For now im working out the problem to the best of my ability.

Answer 6

i dont think its a right triangle

Answer 7

its not a right triangle

Answer 8

I just need to know if the question did state if it is a right angle triangle or not. So just to confirm, the question didnt say right?

Answer 9

no it didnt state it was a right triangle

Answer 10

show work if u can plz

Answer 11

Hold on. Im having some problems.

Answer 12

ok

Answer 13

you get it?

Answer 14

Do you have the answer to the question? because i got 24 and im not sure if i got the right answer.

Answer 15

thats right... will you show how you got that though?

Answer 16

?

Answer 17

Okay :D Np, since i know i am right.

It is really easy, it just tricky and tries to confusing you with all those circle.

Firstly. you need to deduce that POM is a right angled triangle.
Why? Because since O is the center of circle O and the line PO is the tangent to circle N. It has to be right- angled. Also remember circle N is the radius of circle O.

Knowing that POM is a right angled triangle. Your next step is to try a line, from the point O to the point where PM is tangential to circle O. The point where line PM touches circle O, I name it A.

Since the line PM is tangential to circle O, the line i just draw from point O to the new point A , OA bisects the quadrants equally. that means to say, that i now know angle PAO and angle AOM are both 45 degrees.

This shows that the 2 triangles PAO and AOM are both isosceles.

(Note that both PAO and AOM are right-angled triangles because of OA being perpendicular to line PM.)

SO you just need to find the length of OA to know the length of PM because PM is just 2 times the length of OA, ( remember isosceles triangle, both PAO and AOM are equal triangles, since they share one side, which is OA).

The length of OA is also the radius of circle O. The radius of circle O is the diameter of circle N. Since the radius of circle N is 6. THe length of OA is 12.

PM = 2 * OA = 24. Voila.

Answer 18

Sry for the grammatical errors in the beginning, didnt have time to edit those out.

Answer 19

Do you understand? just ask if you have any questions.