0 votes
in Circles by (44.6k points)
closed by

In a circle with centre ‘O’, \(\overline {AB}\) is a chord and M is its midpoint. Now prove that \(\overline {OM}\) is perpendicular to AB. 

(Hint : Join OA and OB consider tri-angles OAM and OBM)

1 Answer

+1 vote
by (45.2k points)
selected by
Best answer

‘O’ is the centre of the circle. 

AB is a chord, M is its midpoint. 

Join A, B to ’O’. 

Now in ΔOMA and ΔOMB 

OA = OB (radii) 

OM = OM (common) 

MA = MB (given) 

∴ ΔOMA s ΔOMB (SSS congruence) 

∴ ∠OMA = ∠OMB (C.P.C.T) 

But ∠OMA and ∠OMB are linear pair 

∴∠OMA = ∠OMB = 90° 

i.e., OM ⊥ AB.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.