Question : Two chords AB and CD of a circle with centre O intersect at P. If $\angle$ APC = 40º, then the value of $\angle$AOC + $\angle$BOD is:
Option 1: 50º
Option 2: 60º
Option 3: 80º
Option 4: 120º

Question

Question : Two chords AB and CD of a circle with centre O intersect at P. If $\angle$ APC = 40º, then the value of $\angle$AOC + $\angle$BOD is:

Option 1: 50º

Option 2: 60º

Option 3: 80º

Option 4: 120º

Team Careers360 · Accepted Answer

Correct Answer: 80º

Solution :
The angle subtended by a chord at the centre is twice the angle subtended on the circumference.
$\angle$BOD = 2$\angle$BCD
⇒ $\angle$AOC = 2$\angle$ABC
⇒ $\angle$AOC + $\angle$BOD = 2($\angle$BCD + $\angle$ABC)
The sum of the interior angle is equal to the exterior angle.
$\angle$BCD + $\angle$ABC = $\angle$APC
⇒ $\angle$AOC + $\angle$BOD = 2$\angle$APC
⇒ $\angle$AOC + $\angle$BOD = 2 × 40º
⇒ $\angle$AOC + $\angle$BOD = 80º
Hence, the correct answer is 80º.

Exams

Colleges

Predictors

Resources

Quick links

Exams

Colleges & Courses

Predictors

Resources

Exams

Colleges

Predictors & E-Books

Resources

Engineering Preparation

Medical Preparation

Online Courses

Products

Exams

Colleges

Resources

Exams

Colleges

Predictors & Articles

Resources

Exams

Colleges

Predictors

Resources

Exams

Colleges

Upcoming Events

Resources

Exams

Colleges

Resources

Quick Links

Top Streams

Specializations

Resources

Top Providers

Exams

Colleges

Resources

Diploma Colleges

Exams

Colleges

Resources

Exams

Resources

Top Courses & Careers

Colleges

Exams

Upcoming Events

Resources

Other Exams

Exams

Colleges

Top Countries

Student Visas

Exams

Top Schools

Products & Resources

NCERT Study Material

Question : Two chords AB and CD of a circle with centre O intersect at P. If ∠ APC = 40º, then the value of ∠AOC + ∠BOD is:Option 1: 50ºOption 2: 60ºOption 3: 80ºOption 4: 120º

Related Questions

Know More about

Upcoming Exams

Trending Articles around SSC CGL

Download the Careers360 App on your Android phone

Sign In/Sign Up

Question : Two chords AB and CD of a circle with centre O intersect at P. If $∠$ APC = 40º, then the value of $∠$ AOC + $∠$ BOD is:
Option 1: 50º
Option 2: 60º
Option 3: 80º
Option 4: 120º