Correct statement related to common tangents of circles

[songoku]

Homework Statement

Please see below

Relevant Equations

(external common tangent)[SUP]2[/SUP] = (distance between center)[SUP]2[/SUP] - (R - r)[SUP]2[/SUP]

Let R = radius of big circle and r = radius of small circle.

I worked out that $R \times r=144$ but then not sure how to proceed. I also know AB = CD = 24 cm.

Thanks

 

[Lnewqban]

If you draw a diagram with very different radii, you could easily see the right answer.
Also, for answering (i), draw the radius that are perpendicular to the tangents for each circle.

 

[songoku]

If you draw a diagram with very different radii, you could easily see the right answer.
Also, for answering (i), draw the radius that are perpendicular to the tangents for each circle.

I understand. The correct answer is (B).

Thank you very much Lnewqban

 

[Lnewqban]

I understand. The correct answer is (B).

Thank you very much Lnewqban

I am not sure about that answer, songoku.
Is it the official correct one?

 

[songoku]

I am not sure about that answer, songoku.
Is it the official correct one?

No, it is not official answer. It is my own answer.

I thought the value of PB and PE will be the same since it is tangent from common point. Same thing for PE and PA so it means that PA = PB = 12 cm.

I used the same reasoning for QD and QE and also QE and QC so QD = QC = 12 cm

Since PE = 12 cm and QE = 12 cm so PQ = 24 cm

Is there something wrong with my working? Thanks

 

[Lnewqban]

No, it is not official answer. It is my own answer.

I thought the value of PB and PE will be the same since it is tangent from common point. Same thing for PE and PA so it means that PA = PB = 12 cm.

I used the same reasoning for QD and QE and also QE and QC so QD = QC = 12 cm

Since PE = 12 cm and QE = 12 cm so PQ = 24 cm

Is there something wrong with my working? Thanks

Your reasoning and working are perfect.
Mine were not.
Thank you!

 

[songoku]

View attachment 346211

Wow, that's amazing.

Thank you very much for the help