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

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Sum

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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Chapter 13: Pythagoras Theorem [Proof and Simple Applications with Converse] - Exercise 13 (A) [Page 159]

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Selina Concise Mathematics Class 9 ICSE
Chapter 13 Pythagoras Theorem [Proof and Simple Applications with Converse]
Exercise 13 (A) | Q 6 | Page 159

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