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 ABC is a right triangle right angled at B such that BC = 6 cm and AB = 8 cm. The radius of its incircle is
  • a)
    3 cm
  • b)
    8 cm
  • c)
    2 cm
  • d)
    5 cm
Correct answer is option 'C'. Can you explain this answer?
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ABC is a right triangle right angled at B such that BC = 6 cm and AB =...
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ABC is a right triangle right angled at B such that BC = 6 cm and AB =...
By pythagoras theorem ,
H2 = P2 + B2
 =36 + 64=100
H=10
We have a square BPOQ so all sides are equal.
Since tangents from a point are equal in length
Let AP = AR = x
BP=BQ=y
RC = QC = z
x + y = 8
x = 8 - y
x + z = 10 ⇒ 8 - y + z = 10 ⇒ z = 2 + y
y + z = 6 ⇒ y + 2 + y = 6 ⇒ y = 2
x = 6, z= 4
Since BP = OQ = y = 2
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ABC is a right triangle right angled at B such that BC = 6 cm and AB = 8 cm. The radius of its incircle is​a)3 cmb)8 cmc)2 cmd)5 cmCorrect answer is option 'C'. Can you explain this answer?
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