wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

In the given figures, O is the centre of the given circles. Match the values of x.

A
40
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
60
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
200
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

In the first image, we see that AB=CD.
We know that equal chords subtend equal angles at the centre.
AOB=COD=40

In the second image, AB=CD and AOB=60.
Since equal chords subtend equal angles at the centre, we have
AOB=COD=60.
Note that s AOB and COD are isosceles.
Thus, using angle sum property in COD, we have
COD+OCD+ODC=180.
60+x+x=180
x=60

In the third image, since OBC is isosceles, we have OBC=OCB=40.
Now, using angle sum property in OCB, we have
40+40+BOC=180BOC=100.
Now, since AB and CB are equal chords, and equal chords subtend equal angles at the centre,
AOB=BOC=100.
Thus, x=AOB+BOC=200.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Equal Chords
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon