## DLS 2 years ago Let C be the circle with centre(0,0) ,radius=3units..The eq.of locus of midpoints of the chords of the circle that substend an angle 2pi/3 at centre=?

1. experimentX

2. DLS

what ismissing?

3. IsTim

Maybe a diagram?

4. IsTim

I'm actually not certain.

5. DLS

not given

6. experimentX

oh!! that would be crystal clear. Are the midpoints of chords subtending 2pi/3 at center?

7. hartnn

|dw:1357461802327:dw| something like this ?

8. shubhamsrg

|dw:1357461806933:dw| distance between (h,k) and center = 3 co60

9. DLS

@experimentX yes

10. DLS

how did we get pi/3?

11. shubhamsrg

|dw:1357461957504:dw| so that'd be half of it,ofcorse.. you can relate this from the fact that both right triangles are congruent..

12. DLS

explain that r=Rcos30 thing :S

13. experimentX

|dw:1357461938365:dw|

14. shubhamsrg

@@experimentX you misunderstood. it says the locus of mid points of all those chords, which subtend angle 2pi/3 at center the chord subtends angle 2pi/3 at the center..

15. experimentX

|dw:1357462092588:dw|

16. DLS

|dw:1357462129634:dw|

17. DLS

R=3 given

18. DLS

|dw:1357462305603:dw|

19. DLS

didnt get why r=Rcos30

20. experimentX

|dw:1357462348001:dw|

21. DLS

then?

22. experimentX

your equation will be a circle with center at 0,0 ... just find the radius using trigonometry.

23. sauravshakya

|dw:1357471539024:dw|

24. sauravshakya

As @experimentX said use trigonometry to find OM

25. sauravshakya

Then find the equation of the circle with center O and radius=OM

26. DLS

Last thing,what will be the radius of the circle(i.e locus) of midpoint of chords?OM?why?

27. experimentX

|dw:1357497953902:dw|

28. DLS

R=3cos 60 yeah ive got that

29. DLS

Is R^2=27/4?

30. DLS

and what is the radius of the locus :/