Two circles with centres M and N have radii 5 cm and 8 cm, respectively. The circles touch each other externally at point T. A line PR is drawn such that the points M, T and N lie on PR, P being closer to M. From P, a tangent PQ = 12 cm is drawn to the circle with centre M touching at Q, and from R, another tangent RS = 15 cm is drawn to the circle with centre N touching at S. What is the length (in cm) of PR?

Correct option is B

Given:
Radius of the circle with center M = 5 cm
Radius of the circle with center N = 8 cm
Tangent PQ = 12 cm
Tangent RS = 15 cm
The circles touch externally at point T.
Formula used: ​

Use the Pythagorean theorem to find PM and NR:

​$$PM^2 = PQ^2 + MQ^2$$​​

For PM:

$$PM² = 12^2 + 5^2$$​ = 144 + 25 = 169

=> PM =√169 = 13 cm

For NR:

NR² = $$15^2 +8^2 = 225 + 64 = 289$$​​

NR = $$\sqrt{289}$$​= 17 cm

Now, distance between M and N:

MN = 5 cm + 8 cm =13 cm

Total length of PR:

Total length of PR = PM + MN + NR

=> PR = 13 cm + 13 cm + 17 cm = 43 cm