Exams › SSC CGL (Prelims) › Maths

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:

1. externally in the ratio 3: 7
2. internally in the ratio 3: 7
3. externally in the ratio 7: 3
4. internally in the ratio 7: 3

Correct answer: externally in the ratio 7: 3

Solution

When the direct common tangents meet the line joining the centres externally, the point divides the segment externally in the ratio of the radii. Since the radii are 7 cm and 3 cm, A divides PQ externally in the ratio 7:3.

Related SSC CGL (Prelims) Maths questions

• 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.
• Two circles of radii 18 cm and 12 cm touch each other externally. Find the length (in cm) of their direct 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 →