7 Views

Question : AB is a chord in a circle with centre O. AB is produced to C such that BC is equal to the radius of the circle. C is joined to O and produced to meet the circle at D. If $\angle \mathrm{ACD}=32^{\circ}$, then the measure of $\angle \mathrm{AOD}$ is _____.

Option 1: 48°

Option 2: 96°

Option 3: 108°

Option 4: 80°


Team Careers360 1st Jan, 2024
Answer (1)
Team Careers360 17th Jan, 2024

Correct Answer: 96°


Solution :
In $\triangle$OBC
OB = BC
So, $\angle$ BOC = $\angle$ BCO = 32°
Also, $\angle$ OBA = $\angle$ BOC + $\angle$ BCO = 32° + 32° = 64°
Since OA = OB
$\angle$ OAB = $\angle$ OBA
In $\triangle$ AOB
$\angle$  AOB + $\angle$  OAB + $\angle$ OBA = 180º
⇒ $\angle$ AOB + 64° + 64° = 180°
⇒ $\angle$ AOB = 180° – 128° = 52°
Now,
$\angle$ AOD + $\angle$ AOB + $\angle$ BOC = 180°
⇒ $\angle$ AOD + 52° + 32°  = 180°
⇒ $\angle$ AOD = 180° – 84° = 96°
Hence, the correct answer is 96°.

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books