Two circles with centres M and N have radii of 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?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 43.
From the given figure
In ΔPQM
⇒ PM2 = PQ2 + QM2
⇒ PM2 = 122 + 52
⇒ PM2 = 144 + 25
⇒ PM2 = 169
⇒ PM = 13 cm
In ΔNSR
⇒ NR2 = NS2 + SR2
⇒ NR2 = 82 + 152
⇒ NR2 = 64 + 225
⇒ NR2 = 289
⇒ NR = 17 cm
Now, the distance between N and M
⇒ MN = 5 + 8 = 13 cm
So,
The total length of PR = PM + MN + NR
⇒ PR = 13 + 13 + 17 = 43 cm