Question : A cyclic quadrilateral ABCD is such that AB = BC, AD = DC and AC and BD intersect at O. If $\angle C A D=46^{\circ}$, then the measure of $\angle A O B$ is equal to:
Option 1: 90°
Option 2: 80°
Option 3: 84°
Option 4: 86°
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 : A cyclic quadrilateral ABCD is such that AB = BC, AD = DC, and AC and BD intersect at O. $\angle$ CAD = 46$^\circ$ ABCD is a cyclic quadrilateral, $\angle$ A + $\angle$ C = $\angle$ B + $\angle$ D = 180$^\circ$ AD = CD ⇒ $\angle$ CAD = $\angle$ DCA = 46$^\circ$ ⇒ $\angle$ ADC = 180$^\circ$ - 92$^\circ$ = 88$^\circ$ ⇒ $\angle$ ABC = 180$^\circ$ - 88$^\circ$ = 92$^\circ$ AB = BC ⇒ $\angle$ BAC = $\angle$ BCA = $\frac{180^\circ-92^\circ}{2}$=$\frac{88^\circ}{2}$ = 44$^\circ$ Now, $\angle$ ABO = $\angle$ DCA = $\angle$ DAC = 46$^\circ$ (angles made by the same arc on the same side of the circle are equal) ⇒ $\angle$ AOB = 180$^\circ$ - (46$^\circ$ + 44$^\circ$) = 90$^\circ$ $\therefore$ $\angle$ AOB is 90$^\circ$ Hence, the correct answer is 90$^\circ$.
Candidates can download this ebook to know all about SSC CGL.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Question : $ABCD$ is a cyclic quadrilateral of which $AB$ is the diameter. Diagonals $AC$ and $BD$ intersect at $E$. If $\angle DBC=35^\circ$, then $\angle AED$ measures _________
Question : ABCD is a cyclic quadrilateral. Sides AB and DC, when produced, meet at E and sides AD and BC, meet at F. If $\angle $ADC = 76$^\circ$ and $\angle$AED = 55$^\circ$, then $\angle$AFB is equal to:
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 : ABC is a right angle triangle and $\angle ABC = 90^{\circ}$. BD is perpendicular on the side AC. What is the value of $(BD)^2$?
Question : ABCD is a cyclic quadrilateral and AD is a diameter. If $\angle$ DAC = 55$^\circ$ then value of $\angle$ABC is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile