The ratio in which a transverse common tangent drawn to two circles with radii 4 cm and 6 cm, respectively, divides the line joining their centres is:
Answer & explanation
Correct answer: option 1
Radius is perpendicular to tangent on circumference of circle. So,
∠P = ∠Q
By using alternate angle theorem ( Because OP is parallel to O'Q )
∠PCO = ∠QCO'
⇒ △PCO ≅ △PCO'
Hence, \(\frac{PO}{QO'}\) = \(\frac{OC}{CO'}\)
We know, \(\frac{PO}{QO'}\) = \(\frac{4}{6}\)
⇒ \(\frac{OC}{CO'}\) = \(\frac{2}{3}\)
So, Required ratio in which transverse line divide the joining line = 2 : 3