Question : 'O' is the circumcentre of triangle ABC lying inside the triangle, then $\angle$OBC + $\angle$BAC is equal to:
Option 1: 90°
Option 2: 60°
Option 3: 110°
Option 4: 120°
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: 90°
Solution : Let $\angle$OBC and $\angle$OCB be $\theta$. In $\triangle$OBC, $\angle$OBC + $\angle$OCB + $\angle$BOC = 180° ⇒ $\theta + \theta + \angle$BOC = 180° ⇒ $\angle$BOC = 180° – 2$\theta$ We know that in a circle, the angle subtended by an arc at the centre is twice the angle subtended by it at the remaining part of the circle. So, $\angle$BOC = 2$\angle$BAC ⇒ $\angle$BAC = $\frac{1}{2} \angle$BOC ⇒ $\angle$BAC = $\frac{1}{2}$ × (180° – 2$\theta$) ⇒ $\angle$BAC = 90° – $\theta$ ⇒ $\angle$BAC = 90° – $\angle$OBC [$\because \angle$OBC = $\theta$] $\therefore \angle$BAC + $\angle$OBC = 90° Hence, the correct answer is 90°.
Candidates can download this ebook to know all about SSC CGL.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Question : Inside a square ABCD, $\triangle$BEC is an equilateral triangle. If CE and BD intersect at O, then $\angle$BOC is equal to:
Question : In $\triangle$ABC, if the median AD = $\frac{1}{2}$BC, then $\angle$BAC is equal to:
Question : In $\triangle$ABC, $\angle$B = 35°, $\angle$C = 65° and the bisector of $\angle$BAC meets BC in D. Then $\angle$ADB is:
Question : G is the centroid of $\triangle$ABC. If AG = BC, then measure of $\angle$BGC is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile