Tayjah 2 years ago theorems related to circles , anyone aware?

1. tanvirms

there are a lot....theorems related to circle and their chords, tangents, angles etc....what do u wanna know?

2. Tayjah

if i was to type a question without the picture would you understand a answer?

3. tanvirms

i can try...go ahead. btw u can draw a picture with the 'draw' tool.

4. Tayjah

ouu YAYA ! . okay one sec

5. Tayjah

|dw:1358257312264:dw| " in the figure, given that point P= point Q . AB=CD , AB=24, and PX=p . what is the length of the given radius Q?

6. tanvirms

where's Q?

7. Tayjah

sorry Q is where P is at on the first circle . you see how i put d twice ? well Q is where P is . get it ?

8. tanvirms

hmm thought so....so u need to find out the radius QY?

9. Tayjah

it just said of Q , but i guess ?

10. tanvirms

can u check the question again? i didnt exactly get what u meant by point P = point Q....how can two points be equal?

11. Tayjah

okay how about i just give you the answer ? , so you can understand how to get it ? ... its 15

12. tanvirms

that'd be only possible if any of the following angles are given. |dw:1358258436102:dw|

13. Tayjah

14. tanvirms

sure...but dont u think we should finish solving it first?

15. tanvirms

|dw:1358259367221:dw|

16. Tayjah

|dw:1358258923677:dw| if point m=point N , AB-CD . QD=24 and ND=26 what is the length of LM?

17. Tayjah

and yes to your last picture

18. tanvirms

what was the given length of the segment that i showed in my last picture??

19. Tayjah

ab=24 and px=9

20. tanvirms

lol and u said PX=p :P :P ok here's the basic theorem, lets say you draw a line from the center of a circle to any chord of the circle, and the angle formed becomes 90 degree |dw:1358259896480:dw| in that case, the point where the line touches the chord will bisect it, so in ur first picture, since AB=24, <x=90, then AX=XB=12 (bisected, halved) and as both the circles are similar, same goes for circle Q too. now, its simple pythagorean theorem |dw:1358260014603:dw| is it clear now?

21. Tayjah

yay and yes . ready for the next one?

22. Tayjah

okay the next one is the picture i sunt you

23. tanvirms

ok let me explain the second one. as you can see, ND=MB=26 is the radius for both the circles. QD is already given (you dont need to halve the chord like u did before, QD is already half), also. QD=LB now use pythagorean theorem to find out LM |dw:1358260511366:dw|