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In the figure, point P and Q lie on the circle with center [#permalink]
03 Sep 2007, 08:07

In the figure, point P and Q lie on the circle with center O. What is the value of S?

A) 1/2
B)1
C) sqrt 2
D) sqrt 3
e) sqrt2 / 2

If you draw a line perpendicular from Point P and Q to x-axis, you can see that the two triangle are congruent. My answer is D. The OA is B. Why is that?

Attachments

Half Circle copy.jpg [ 15.24 KiB | Viewed 658 times ]

i see what you mean, i believe both triangles are congruent triangles, with 30, 60 and 90. but the triangle from the left has its 30C angle attached to the centre O and the triangle on the left has its 60C angle attached to centre O.

From the left we have a triangle: 1-sqrt3-2, so radius = 2.
Triangle in the middle is a right triangle with the legs = radius = 2
From the right we have a triangle 1-sqrt3-2, but the leg sqrt3 is situating opposite 60 degree angle and is a vertical line. So S coordinate of this point = 1

Last edited by Whatever on 03 Sep 2007, 20:57, edited 4 times in total.

A triangle that has two sides equal has two adjacent angles equal, since PO=OQ; angle QPR=anglePQO.

The angle between PO and QO is 90, leaving 90 {180 -90} degrees for the other two EQUAL angles.

Thus 90/2 is 45 degrees each angle

45:45:90

sum of angles of any tiangle is 180.

Don't be tricked by the figure:

"Thus 90/2 is 45 degrees each angle" this is incorrect.

It takes be awhile to see this, if you re-draw the graph yourself and have the up-side-down triangle slightly tited to your left.

Yeah, of course,

The the upper part of coordinate system is devided into 30,90 and 60 degrees. and the triagles are not symmetric.
I was saying that the triangle that PQO {that is the one we get when we connect P and Q} is 90:45:45

A triangle that has two sides equal has two adjacent angles equal, since PO=OQ; angle QPR=anglePQO.

The angle between PO and QO is 90, leaving 90 {180 -90} degrees for the other two EQUAL angles.

Thus 90/2 is 45 degrees each angle

45:45:90

sum of angles of any tiangle is 180.

Don't be tricked by the figure:

"Thus 90/2 is 45 degrees each angle" this is incorrect.

It takes be awhile to see this, if you re-draw the graph yourself and have the up-side-down triangle slightly tited to your left.

Yeah, of course,

The the upper part of coordinate system is devided into 30,90 and 60 degrees. and the triagles are not symmetric. I was saying that the triangle that PQO {that is the one we get when we connect P and Q} is 90:45:45