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 ______.
Option 1: $6 \sqrt{27}\ \text{cm}$
Option 2: $9 \sqrt{27}\ \text{cm}$
Option 3: $\sqrt{3}\ \text{cm}$
Option 4: $3 \sqrt{3}\ \text{cm}$
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: $6 \sqrt{27}\ \text{cm}$
Solution : Given: Two equal circles of radius $18\ \text{cm}$ intersect each other. From the given figure, $AD = DB$ (the perpendicular from the centre of a circle to a chord bisects the chord) and $OC = OA = CA =\text{Radius}= 18\ \text{cm}$ $\angle ADO = 90°$ $OD = DC = 9$ cm ( Half the radius) Using Pythagoras' theorem in $\triangle ADC,$ $(AC)^2 = (AD)^2 + (DC)^2$. $⇒(18)^2 = (AD)^2 + (9)^2$ $⇒324 = (AD)^2 + 81$ $⇒(AD)^2 = 324 – 81$ $⇒(AD)^2 = 243$ $⇒AD=3\sqrt{27}\ \text{cm}$ The common chord's length is $AB = 2×AD$ $AB = 2×3\sqrt{27}= 6\sqrt{27}\ \text{cm}$ Hence, the correct answer is $6\sqrt{27}\ \text{cm}$.
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 : Two circles touch each other externally. The radius of the first circle with centre O is 6 cm. The radius of the second circle with centre P is 3 cm. Find the length of their common tangent AB.
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 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.
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?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile