Question

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

Answer 1

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`