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

Let us assume, AO = y and OC = x
Using Pythagoras theorem, In a Right-angled triangle AOC we have
AO²+ OC²= AC²
⇒ y²+x²=3²
∴ y² = 9 − x²

Using Pythagoras theorem, In a Right-angled triangle AOB we have
AO²+ OB² = AB²
⇒ y² + (x + 6)²= 8²
⇒ 9 − x² + x²+ 12x + 36 = 64
⇒ 12x + 45 = 64
⇒ 12x = 64 – 45 = 19
⇒ x = 1.58 cm
Hence OC = 1.58 cm

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