The length of common tangent to the circle of radii 12 cm and 4cm is 15 cm.Find the distance between their centres

Asked by lovemaan5500 | 24th Dec, 2017, 03:44: PM

Expert Answer:

begin mathsize 16px style Consider space two space circles space of space radii space 12 space cm space and space 4 space cm space with space centre space straight B space and space straight A space respectively.
Length space of space direct space common space tangent space to space both space the space circles space is space 15 space cm.
CD equals 15 space cm
CD equals BE equals 15 space cm
AE equals AC minus CE
AE equals 12 space minus space 4 space equals space 8 space cm
AB equals straight x space cm
In space the space right space triangle space BEA comma
using space Pythagoras
BE squared plus EA squared equals BA squared
straight x squared equals 8 squared plus 15 squared
straight x squared equals 289
straight x equals 17 space cm
Distance space between space the space centres space of space two space circles space is space 17 space cm. end style

Answered by Sneha shidid | 24th Dec, 2017, 08:26: PM