Perpendicular sector problem
In a circle, two perpendicular sector intersects the yellow circle at 4 point. Then red=6cm and blue=8cm lines drawn. Find the radius of the circle?
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
3 solutions
Let the center of the circle be O , the end points of the line segment of length 8 cm. be A and C , those of 6 cm. line segment be D and E and the right angle be at B . Let the radius of the circle be R and ∠ O A C = ∠ O C A = α . Then ∠ D O E = 2 α . So, 2 R sin α = 6 , 2 R cos α = 8 ⟹ R = 3 2 + 4 2 = 2 5 = 5 cm.
good solution sir!
Can you please show through a diagram relation between angles OAC and DOE ? Thanks.
nice approach!
I think you assume red and blue triangles are similar ! They can not be. Angles by chords 6 and 8 can not be equal.
Please correct me if I am wrong.
Your equation 3 4 8 + 2 8 = y 2 a c c o r d i n g t o m e i t i s 1 2 n o t 2 8 . A c c i d e n t a l l y i t s e e m s t w o m i s t a k e s c a n c e l t o g i v e c o r r e c t a n s w e r ! ! !
Log in to reply
@Niranjan Khanderia Sir, waiting for your solution. ;) what's your opinion about my approach.
Log in to reply
Yours is the best and the only correct approach.
My approach was to assume 8 and 6 to be ||. That gives the answer but is not the correct solution since it assumes
what is not given. It could be a special case. I am trying to find a correct solution other than your solution.
Log in to reply
@Niranjan Khanderia – Approbation! That means a lot sir! And I'm sure you will find a better approach than mine. cheers!