## xRAWRRx3 3 years ago Please help :( Given: Circle O with tangent PA , secant PBC, diameter DOE, and chord AC. PA = 20, PB = 8, AF = CF, measure angle APC = 49, and measure of arc AB = 41. Please help me find the measure of angle COD.

1. xRAWRRx3

|dw:1338705728728:dw|

2. dpaInc

are the angle measure and arc measures are in degrees?

3. xRAWRRx3

yes.

4. Callisto

Angle AOB = 41 degrees angle AOC = 180 - 41 degrees = 139 degrees (adj. angles on st. line) Since AF = FC . OD is perpendicular to AC (line joining from centre perpendicular to chord bisects chord) and triangle AOC is an isos triangle angle AOD = angle DOC = angle AOC / 2 = 139/2 = ... ?

5. dpaInc

69.5??? |dw:1338706212875:dw|

6. shubhamsrg

i'll give you hints : (altough i find some info to be useless in the ques) use these things : 1)join OA 2) if a line from the center bisects a chord,that line is perpendicular to the chord 3)a perpendicular to the opposite side in an isosceles triangle bisects the angle in between 4)tangent and radius are perpendicular 5)sum of angles in a triangle = 180 6)sum of linear angles =180 you should get your ans then..

7. shubhamsrg

8. xRAWRRx3

yeahh, pretty much. But thanks, everyone, for helping me x) You all helped me understand the problem a little bit more so thank you x)

9. xRAWRRx3

I wish I can give medals to you all but sadly, I can't :(

10. dpaInc

no...it was @Callisto ... :) wish i could take credit though...

11. Callisto

You guys make it too.... complicated :|

12. dpaInc

:) that's what we do....

13. shubhamsrg

oh yes..i missed @Callisto post...hmnn..