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**In triangle ABC, given below, AB = 8 cm, BC = 6 cm and AC = 3 cm. Calculate the length of OC.**

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#### Solution

We have Pythagoras theorem which states that in a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the remaining two sides.

In Δ AOC,

AC^{2} = AO^{2} + CO^{2}

(3)^{2} = AO^{2 }+ x^{2}

9 = AO^{2 }+ x^{2 }

9 - x^{2 }= AO^{2 } ...(i)

In Δ AOB,

AB^{2} = AO^{2} + BO^{2 }

(8)^{2} = AO^{2 }+ (6 + x)^{2 }

64 = AO^{2 }+ (6 + x)^{2}

64 - (6 + x)^{2} = AO^{2 } ...(ii)

From equation (i) and (ii)

9 - x^{2 }= 64 - (6 + x)^{2 }

9 - x^{2 }= 64 - (36 + x^{2} + 12x) ...[(a + b)^{2} = a^{2} + 2ab + b^{2}]

9 - x^{2 }= 64 - 36 - x^{2} - 12x

9 = 28 - 12x

12x = 28 - 9

x = `19/12`

x = `1 7/12`

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