Question
Download Solution PDFIn the following figure, the circles with centres B and D have radii 4 cm and x cm, respectively. AC is a tangent to both the circles. Find the value of x.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Radius of small circle (r) = 4 cm
AE = 6 cm; EC = 9 cm
Concept used:
The tangent makes a right angle with the radius of a circle at the point of contact.
The vertical opposite angle is equal.
Calculation:
AD ⊥ AC and BC ⊥ AC
∠DAE = ∠BCE = 90°
In △DAE and △BCE
∠DAE = ∠BCE = 90°
∠AED = ∠BEC (Vertical angle)
△DAE ∼ △BCE (By AA similarity)
By C.P.C.T
⇒ AE/EC = AD/BC
⇒ 6/9 = 4/BC
⇒ BC = 36/6 = 6 cm
∴ The correct answer is 6 cm.
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