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Re: Let S be a point on a circle whose center is R. If PQ is a c [#permalink]
1
So, PQ goes thru RS. We join radii to PQ from R and we get two triangles. As all radii are same size we join PS and SQ segments. O is teh center where thru PQ goes thru RS.
PR = RQ and RO common. In addition, and hence PO = OQ. We get 30/60/90 triangle. Hence angle at center is 120

Proportion --> 120/360 *2PieR --> 1/3 2 pie R.
1/3 *2pie R/ 2Pie (R)(this the is entire circle) --> 1/3 is answer

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Re: Let S be a point on a circle whose center is R. If PQ is a c [#permalink]
Carcass wrote:
Let S be a point on a circle whose center is R. If PQ is a chord that passes perpendicularly through the midpoint of RS, then the length of arc PSQ is what fraction of the circle’s circumference?

A. \(\frac{1}{\pi}\)

B. \(\frac{1}{3}\)

C. \(\frac{3}{\pi+2}\)

D. \(\frac{1}{2 \sqrt{2}}\)

E. \(\frac{2 \sqrt{3} }{3 \pi}\)


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SIr, can you please elaborate it in a better way? cause no one can provide like you GreenlightTestPrep
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Re: Let S be a point on a circle whose center is R. If PQ is a c [#permalink]
GreenlightTestPrep wrote:
Carcass wrote:
Let S be a point on a circle whose center is R. If PQ is a chord that passes perpendicularly through the midpoint of RS, then the length of arc PSQ is what fraction of the circle’s circumference?

A. \(\frac{1}{\pi}\)

B. \(\frac{1}{3}\)

C. \(\frac{3}{\pi+2}\)

D. \(\frac{1}{2 \sqrt{2}}\)

E. \(\frac{2 \sqrt{3} }{3 \pi}\)


Here's what the diagram looks like:
Image

From here let's add lines from the center (R) to P and Q.
At the same time, let's say the radius of the circle is 2, which means we get the following measurements:
Image

We now have two small right triangles in our diagram.
Since we know the length of two of the three sides, we can apply the Pythagorean theorem to find the length of the third sides:
Image

Notice that the two right triangles have the lengths 1, 2, and √3, which are the lengths of the base 30-60-90 right triangle.
This means we add the following angles to our diagram:
Image

We can now see that angle PRQ = 120°
The entire circumference of the circle encompasses an angle of 360°

So the fraction of the circumference occupied by arc PSQ = 120°/360° = 1/3

Answer: B


Now it is crystal clear. These days I have addiction to see that how you change complex one into very easy. :heart :heart
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Re: Let S be a point on a circle whose center is R. If PQ is a c [#permalink]
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