# If two circles in

Let two circles O and O' intersect at two points A and B so that AB is the common chord of two circles.

OO' is the line segment joining the centers.
Let OO' intersect AB at M
Now Draw line segments OA, OB , O'A and O'B
In ΔOAO' and OBO' , we have
OA = OB (radii of same circle)
O'A = O'B (radii of same circle)
O'O = OO' (common side)
ΔOAO' ΔOBO' (SSS congruency)
AOO' = BOO'
AOM = BOM ......(i)
Now in ΔAOM and ΔBOM we have
OA = OB (radii of same circle)
AOM = BOM (from (i))
OM = OM (common side)
ΔAOM ΔBOM (SAS congruency)
AM = BM and AMO = BMO
But
AMO + BMO = 180°
2AMO = 180°
AMO = 90°
Thus, AM = BM and
AMO = BMO = 90°
Hence OO' is the perpendicular bisector of AB.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Arc of Circle And Related IMP Qs40 mins
IMP Qs Related with Circles For Boards44 mins
Chords Of Circles42 mins
IMP Theorems And Their Application43 mins
Circles- All kinds of Questions36 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

Name the followinAP- Mathematics

Draw two circles AP- Mathematics

State true or falAP- Mathematics

If two circles inAP- Mathematics

Draw a circle witAP- Mathematics