Circles and Arcs

Thouraya wrote:Hi,

I would appreciate it if one of the experts may help on the below:

I have a circle with center O and angle POQ=90 degrees (with P and Q being on the circle). If we have O=90 degrees, and length of PQ is 4 pie, how can we find the radius?


I am actually still finding it confusing sometimes how to solve the problems that revolve around circles and arcs. I am aware of the two formulas for length and area, but sometimes I get lost when to use which. Also, when shall I use the concept that says that the area of an arc is equal to twice its angle?

Appreciated!

This is simple. If you know length of Arc formula, you sould be able to arrive at the answer.

Lengh of arc = (x/360) * 2pi* R
=90/360 * 2Rpi
=Rpi/2

Now Rpi/2 = 4pi
R/2 =4
R=8

Hope this helps!!

Thouraya wrote: I have a circle with center O and angle POQ=90 degrees (with P and Q being on the circle). If we have O=90 degrees, and length of PQ is 4 pie, how can we find the radius?

Hold on, are you sure PQ is refering to the arc? From the wording of the question it sounds like PQ is (or could be) the chord PQ. In that case, POQ is an isosceles right triangle with PQ as the hypotenuse.

If the legs of an isosceles right triangle each have a length of x, the hypotenuse is x root 2 (xV2). Therefore the length of the radius (leg) is 4pi / V2, which simplifies to 2V2pi.

Hi Nicole,


Thanks for ur post.

Yes, it is true. You may assume that PQ is a chord because points P and Q lie on the circle; thus, as you said triangle OPQ is a right isoceles triangle; however I am not sure you can use the approach u used here...Usually, and as far as I am aware, we use this if we already have the length of the radius, and want to look up PQ (thus use pythagoren);however, GMat Titan's reply above is correct I guess (I dont have the official answer with me).

I would appreciate if one of the experts may help. I still have the questions: When should I use the formula that an arc is double its interior angle...?

Thank u!

I believe PQ here is length of arc, for two reasons:
1. If PQ is the chord lenth, it would explicitly be mentioned in the qustion.
2. PQ is given as 4Pi. Normally, only Arcs' length will be mentioned in multiples of pi.

Hope this helps!!