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Question
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,
AC2 = AO2 + CO2
(3)2 = AO2 + x2
9 = AO2 + x2
9 - x2 = AO2 ...(i)
In Δ AOB,
AB2 = AO2 + BO2
(8)2 = AO2 + (6 + x)2
64 = AO2 + (6 + x)2
64 - (6 + x)2 = AO2 ...(ii)
From equation (i) and (ii)
9 - x2 = 64 - (6 + x)2
9 - x2 = 64 - (36 + x2 + 12x) ...[(a + b)2 = a2 + 2ab + b2]
9 - x2 = 64 - 36 - x2 - 12x
9 = 28 - 12x
12x = 28 - 9
x = `19/12`
x = `1 7/12`
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