There are two circles of radius 5 cm and 3 cm respectively. The distance between their centres is 10 cm. The length (in cm) of a direct common tangent is:
Show answer & explanation
Correct answer: B
Explanation
Correct Answer is option 2 i.e. 4√6 cm
Given,
Radius of circle A = AO = 5 cm,
Radius of circle B = BC = 3 cm
Distance between the centres of the two circles = OC = 10 cm.
AB is the direct common tangent.
In the figure,
By Pythagoras theorem, we get
CD = √(OC2 – OD2)
⇒ CD = √(102 – 22)
⇒ CD = √(100 – 4)
⇒ CD = √96
⇒ CD = 4√6
Hence, tangent AB = CD = 4√6 cm