Question
Download Solution PDFTwo 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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:
PM2 = PQ2 + MQ2
NR2 = RS2 + NS2
Total length of PR = PM + MN + NR
Calculations:
For PM:
PM2 = 122 + 52
⇒ PM2 = 144 + 25
⇒ PM2 = 169
⇒ PM = √169 = 13 cm
For NR:
NR2 = 152 + 82
⇒ NR2 = 225 + 64
⇒ NR2 = 289
⇒ NR = √289 = 17 cm
Now, distance between M and N:
MN = 5 cm + 8 cm = 13 cm
Total length of PR:
PR = PM + MN + NR
⇒ PR = 13 cm + 13 cm + 17 cm = 43 cm
∴ The length of PR is 43 cm.
Last updated on May 28, 2025
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