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In the fig. ABC is right triangle right angled at B such that BC = 6cm and AB = 8cm. Find the radius of its in circle.
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BC = 6cm AB = 8cm
As ABC is right angled triangle
By Pythagoras theorem
ЁЭР┤ЁЭР╢2 = ЁЭР┤ЁЭР╡2 + ЁЭР╡ЁЭР╢2 = 62 + 82 = 100
ЁЭР┤ЁЭР╢ = 10 ЁЭСРЁЭСЪ
Consider BQOP ∠B = 90°,
∠BPO = ∠OQB = 90° [At point of contact, radius is perpendicular to tangent]
All the angles = 90° & adjacent sides are equal
∴ BQOP is square BP = BQ = r
We know that
The tangents drawn from any external point are equal in length.
AP = AR = AB – PB = 8 – r
QC = RC = BC – BQ = 6 – r
AC = AR + RC ⇒ 10 = 8 – r + 6 – r
⇒ 10 = 14 – 2r
⇒ 2r = 4
⇒ Radius = 2cm
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