Seems like my assumption about the right angle at the center 0 was wrong. If not, how else are we going to find the value of point s - given the seemingly obvious answer -- D -- is wrong. Question: In the figure ahove, points P and Q lie on the circle with center 0. What is the value of s ? A- 1/2 B- 1 C- sqrt(2) D- sqrt(3) E- sqrt(2)/2

I've recently been given this solution: t/s*(-1/root(3)) = -1 ---> since lines OP and OQ are perpendicular also let s^2+t^2=r^2=3+1=4 ---> (since P lies on the same circle and O is origin) solve for s s^2+3s^2=4 => s=+/-1

LevelOne wrote:I've recently been given this solution: t/s*(-1/root(3)) = -1 ---> since lines OP and OQ are perpendicular also let s^2+t^2=r^2=3+1=4 ---> (since P lies on the same circle and O is origin) solve for s s^2+3s^2=4 => s=+/-1 how did u replace t^2 with 3s^2 ? Can u expand more on your first solution, if u can please.

abhinav85 wrote:IMO B ok, how ?

IMO you don't need any math here to solve the problem. you can notice in the diagram, to be a 90 degree angle, the two points must be in reverse order with respect to the quadrant they are in. think about (1,0 and 0,1) the angle b/w them is 90 degrees. The same with (-1,0) and (0,1). here the semi-circle is in two quads. the point (s) is in the first quad which means it is positive. since the point given is [-sqrt(3),1], (s,t) would be the reverse with respect to the first quadrant. [1, sqrt(3)] would be (s,t) in this case, which would make s = 1. hope that made sense. if you are looking for a more mathematical approach, you can find it by making two 30-60-90 triangles with the x axis. Check out the link below. https://www.beatthegmat.com/what-is-the- ... 27181.html

ssmiles08 wrote:IMO you don't need any math here to solve the problem. you can notice in the diagram, to be a 90 degree angle, the two points must be in reverse order with respect to the quadrant they are in. think about (1,0 and 0,1) the angle b/w them is 90 degrees. The same with (-1,0) and (0,1). here the semi-circle is in two quads. the point (s) is in the first quad which means it is positive. since the point given is [-sqrt(3),1], (s,t) would be the reverse with respect to the first quadrant. [1, sqrt(3)] would be (s,t) in this case, which would make s = 1. hope that made sense. if you are looking for a more mathematical approach, you can find it by making two 30-60-90 triangles with the x axis. Check out the link below. https://www.beatthegmat.com/what-is-the- ... 27181.html Thanks for pointing this link !