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.
Option 1: $3\sqrt{2}$ cm
Option 2: $4\sqrt{2}$ cm
Option 3: $6\sqrt{3}$ cm
Option 4: $6\sqrt{2}$ cm
Latest: SSC CGL Tier 1 Result 2024 Out | SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL Tier 1 Scorecard 2024 Released | SSC CGL complete guide
Suggested: Month-wise Current Affairs | Upcoming Government Exams
Correct Answer: $6\sqrt{2}$ cm
Solution : $R{_{C{_1}}} = 6$ cm $R{_{C{_2}}} = 3$ cm To find the length of the common tangent. Length of direct common tangent = $\sqrt{d^2 - (R{_{C{_1}}} - R{_{C{_2}}})^2}$ Where $d = R{_{C{_1}}} + R{_{C{_2}}} = 9$ cm $\therefore$ Length of common tangent $ = \sqrt{9^2 - (6 - 3)^2}$ $= \sqrt{81-3^2} = \sqrt{81-9} = \sqrt{72} = 6\sqrt2$ cm Hence, the correct answer is $6\sqrt2$ cm.
Candidates can download this ebook to know all about SSC CGL.
Result | Eligibility | Application | Selection Process | Preparation Tips | Admit Card | Answer Key
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 : There are two circles which touch each other externally. The radius of the first circle with centre O is 17 cm and the radius of the second circle with centre A is 7 cm. BC is a direct common tangent to these two circles, where B and C are points on the circles with centres O
Question : Two circles of radius 10 cm and 5 cm touch each other externally at point A. PQ is the direct common tangent of those two circles of centres O1 and O2, respectively. The length of PQ is equal to:
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 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?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile