Question : Two identical circles each of radius 30 cm intersect each other such that the circumference of each one passes through the centre of the other. What is the area of the intersecting region?
Option 1: $400 \pi-250 \sqrt{3} \mathrm{~cm}^2$
Option 2: $300 \pi-150 \sqrt{3} \mathrm{~cm}^2$
Option 3: $500 \pi-350 \sqrt{3} \mathrm{~cm}^2$
Option 4: $600 \pi-450 \sqrt{3} \mathrm{~cm}^2$
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: $600 \pi-450 \sqrt{3} \mathrm{~cm}^2$
Solution : OA = O’A = OB = OB’ = OO’ = 30 cm In triangle AOO’, OA = O’A = OO’ = 30 cm ( As all three sides of AOO' are equal, so it is an equilateral triangle) ⇒ $∠AOO’ = 60°$ ⇒ $∠AOB = 120°$ In triangle ACO, $AC^2 = OA^2 - OC^2 =30^2-15^2= 900 - 225$ ⇒ $AC^2 = 675$ ⇒ $AC = 15\sqrt3$ So, $AB = 30\sqrt3$ Area of AO’BA = Area of sector AO’BO $-$ Area of triangle AOB = $=\frac{\pi(30)^2}{3}-\frac{1}{2}\times 30\sqrt3\times 15$ $=\frac{900π}{3}- 225\sqrt3$ $=300π - 225\sqrt3$ $\therefore$ Area of intersecting region = 2(Area of AO’BA) $=600π - 450\sqrt3$ cm 2 Hence, the correct answer is $600π - 450\sqrt3$ cm 2 .
Candidates can download this ebook to know all about SSC CGL.
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Question : Two circles each of radius 36 cm are intersecting each other such that each circle passes through the centre of the other circle. What is the length of the common chord to the two circles?
Question : Three circles of radius 6 cm each touch each other externally. Then the distance of the centre of one circle from the line joining the centres of the other two circles is equal to:
Question : Two equal circles of radius 18 cm intersect each other, such that each passes through the centre of the other. The length of the common chord is ______.
Question : Two circles of the same radius 6 cm, intersect each other at P and Q. If PQ = 10 cm, then what is the distance between the centres of the two circles?
Question : Two circles touch each other externally. The radius of the first circle with centre O is 12 cm. Radius of the second circle with centre A is 8 cm. Find the length of their common tangent BC.
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile