Question : In the following figure, AB is the diameter of a circle whose centre is O. If $\angle AOE=150^{\circ},\angle DAO=51^{\circ}$ then the measure of $\angle CBE$ is:
Option 1: 115°
Option 2: 110°
Option 3: 105°
Option 4: 120°
Correct Answer: 105°
Solution : According to the given figure in question, Given $\angle$AOE = 150° and $\angle$DAO = 51° Now, $\angle$EOB + $\angle$AOE = 180° ⇒ $\angle$EOB = 180° – 150° = 30° Also, OE = OB ⇒ $\angle$OEB = $\angle$OBE = $\frac{150}{2}$ = 75° ⇒ $\angle$CBE = 180° – 75° = 105° Hence, the correct answer is 105°.
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
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 _____.
Question : ABCD is a cyclic quadrilateral such that AB is the diameter of the circle circumscribing it and $\angle $ADC = 118°. What is the measure of $\angle$BAC?
Question : ABCD is a cyclic quadrilateral such that AB is the diameter of the circle circumscribing it and $\angle A D C=148^{\circ}$. What is the measure of the $\angle BAC$?
Question : Circum-centre of $\triangle PQR$ is O. If $\angle QPR=55^{\circ}$ and $\angle QRP=75^{\circ}$, What is the value (in degree) of $\angle OPR$?
Question : In a triangle, ABC, BC is produced to D so that CD = AC. If $\angle BAD=111^{\circ}$ and $\angle ACB=80^{\circ}$, then the measure of $\angle ABC$ is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile