Question : In the given figure, if $\mathrm{PA}$ and $\mathrm{PB}$ are tangents to the circle with centre $\mathrm{O}$ such that $\angle \mathrm{APB}=54^{\circ}$, then $\angle \mathrm{OBA}=$________.
Option 1: 27°
Option 2: 40°
Option 3: 30°
Option 4: 35°
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: 27°
Solution : We have to find $\angle AOB$. In quadrilateral APBO, $\angle A = \angle B = 90°$ Now, $\angle P + \angle A + \angle B + \angle O = 360°$ ⇒ $54° + 90° + 90° + \angle O = 360°$ ⇒ $\angle O = 126°$ Now, in $\triangle AOB$ $\angle OBA + \angle OAB + \angle AOB = 180°$ Now, $\angle OBA$ and $\angle OAB$ will be equal as the tangents subtends equal angles. ⇒ $2\angle OBA = 180° - 126°$ ⇒ $2\angle OBA = 54°$ ⇒ $\angle OBA = 27°$ Hence, the correct answer is 27°.
Candidates can download this ebook to know all about SSC CGL.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Question : In the given figure, $\mathrm{O}$ is the centre of the circle and $\angle\mathrm{AOB}=130^{\circ}$. Find $\angle\mathrm{APB}$.
Question : AB is a chord in the minor segment of a circle with centre O. C is a point on the minor arc (between A and B ). The tangents to the circle at A and B meet at a point P. If $\angle \mathrm{ACB}=108^{\circ}$, then $\angle \mathrm{APB}$ is equal to:
Question : In the given figure, $\angle ABC=81^{\circ}$ and $\angle ACB=9^{\circ}$. What is the value of $\angle BDC$?
Question : In the given figure, $\angle D B C=65^{\circ}, \angle B A C=35^{\circ}$ and $\mathrm{AB}=\mathrm{BC}$, then the measure of $\angle \mathrm{ECD}$ is equal to: 3 Views
Question : In the given figure, $O$ is the centre of the circle and $\angle AOC=140°$. Find $\angle ABC$.
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile