In the following figure, the circles with centres B and D have radii 4cm and x cm, respectively. AC is a tangent to both circles. Find the values of x.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 6.
In the given figure, AD is perpendicular to AC and BC is perpendicular to AC.
In triangles DAE and BCE,
∠DAE = ∠BCE = 90°
∠DEA = ∠BEC (Vertically opposite angle)
Triangle DAE is similar to triangle BCE.
⇒ AE/CE = AD/BC
⇒ 6/9 = 4/x
⇒ x = 36/6
⇒ x = 6 cm