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Question
In the given figure, \Delta ABC is right-angled at B such that BC = 6 cm and AB = 8 cm. A circle with centre O has been inscribed inside the triangle. OP ⊥ AB, OQ ⊥BC and OR ⊥ AC. if OP = OQ = OR = x cm then x = ?
(a) 2 cm (b) 2.5 cm
(c) 3 cm (d) 3.5 cm
In the given figure, \Delta ABC is right-angled at B such that BC = 6 cm and AB = 8 cm. A circle with centre O has been inscribed inside the triangle. OP ⊥ AB, OQ ⊥BC and OR ⊥ AC. if OP = OQ = OR = x cm then x = ?
(a) 2 cm (b) 2.5 cm
(c) 3 cm (d) 3.5 cm
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Solution
In right triangle BAC
BC2=AB2+AC2 [By Pythagoras theorem]
= 62 + 82
= 36 + 64
= 100
Hence BC = 10 cm
Semi-perimeter, s = (a + b + c)/2
= (6 + 8 + 10)/2 = 12 cm
Area of right triangle ABC = (1/2) x AB x AC
= (1/2) x 6 x 8 = 24 sq cm
We know that, area of triangle, Δ = r x s
That is 24 = r x 12
Therefore r = 2 cm
In right triangle BAC
BC2=AB2+AC2 [By Pythagoras theorem]
= 62 + 82
= 36 + 64
= 100
Hence BC = 10 cm
Semi-perimeter, s = (a + b + c)/2
= (6 + 8 + 10)/2 = 12 cm
Area of right triangle ABC = (1/2) x AB x AC
= (1/2) x 6 x 8 = 24 sq cm
We know that, area of triangle, Δ = r x s
That is 24 = r x 12
Therefore r = 2 cm
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