Question : In the given diagram, an incircle DEF is circumscribed by the right-angled triangle in which AF = 6 cm and EC = 15 cm. Then find the difference between CD and BD.
Option 1: 1 cm
Option 2: 3 cm
Option 3: 4 cm
Option 4: 5 cm
Correct Answer: 1 cm
Solution :
Since tangents drawn from a point to the circle are equal,
AF = AE = 6 cm
EC = CD = 15 cm
Let BF = BD = $x$
By Pythagoras theorem,
BA
2
+ AC
2
= BC
2
⇒$(6+x)^2+ (6+15)^2 = (15+x)^2$
⇒ $36+x^2+12x+ 441 = 225+x^2+30x$
⇒ $18x = 252$
⇒ $x = 14$
Difference between CD and BD = 15 – 14 = 1 cm
Hence, the correct answer is 1 cm.
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