A circle of radius 4cm is drawn inscribed in a right angle triangle ABC, right angled at C. If AC = 12 cm, then the value of CB is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 16 cm.
According to the given question,
The length of the tangents from the same point are equal.
Using Pythagoras theorem in triangle ABC,
AB2 = BC2 + AC2
⇒ (8 + x)2 = (4 + x)2 + 122
⇒ x2 + 16x + 64 = x2 + 8x + 16 + 144
⇒ 8x = 96
⇒ x = 12
Now, CB = x + 4
⇒ CB = 12 + 4
⇒ CB = 16 cm