Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
603 views
in Circles by (27.3k points)
closed by

O is the circumcentre of the triangle ANC and OD is perpendicular on BC. Prove that ∠BOD= ∠A

1 Answer

+1 vote
by (26.9k points)
selected by
 
Best answer

Given that, 

O is the circumcentre of triangle ABC and OD perpendicular BC 

To prove : 

∠BOD = ∠A 

Proof : 

In triangle OBD and triangle OCD, we have 

∠ODB = ∠ODC (Each 90°) 

OB = OC (Radii) 

OD = OD (Common) 

By R.H.S rule,

ΔODB ≅ ΔODC

∠BOD = ∠COD (By c.p.c.t) ...(i) 

By degree measure theorem, 

∠BOC = 2∠BAC 

2∠BOD = 2∠BAC [From (i)] 

∠BOD = ∠BAC 

Hence, proved

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.

Categories

...