Exams › SSC CGL (Prelims) › Maths
Two circles of radii 18 cm and 12 cm touch each other externally. Find the length (in cm) of their direct common tangent.
- 15√6
- 10√6
- 12√6
- 18√6
Correct answer: 12√6
Solution
Since the circles touch externally, the distance between their centers is 18 + 12 = 30 cm. For a direct common tangent, length = \(\sqrt{30^2-(18-12)^2}=\sqrt{900-36}=\sqrt{864}=12\sqrt{6}\).
Related SSC CGL (Prelims) Maths questions
- P and Q are the centres of two circles whose radii are 7 cm and 3 cm, respectively. If the direct common tangents to the circles meet PQ extended at A, then A divides PQ:
- The radii of two circles are 5 cm and 10 cm, and the distance between their centres is 17 cm. Find the length of the transverse common tangent.
- X, Y, and Z are three points on a plane with \(XY = 11\) cm, \(YZ = 13\) cm, and \(XZ = 24\) cm. The number of circles passing through points X, Y, and Z is:
- A number whose fifth part increased by 5 is equal to its third part decreased by 7. Find half of the number.
- If (48^ + k) is an acute angle and sin(48^ + k) = cos 13^, what is the value of k (in degrees)?
- If ₹1,875 becomes ₹2,625 in 4 years, what will ₹24,000 become at the end of 9 years at the same rate of interest, under simple interest?
⚔️ Practice SSC CGL (Prelims) Maths free + battle 1v1 →