Question

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

• A. $5.6cm$
• B. $2.6cm$
• C. $3.6cm$
• D. $1.6cm$

Answer 1

Answer: (D)

By Phythagoras theorem,

In $△ABO,A{B}^2=A{O}^2+B{O}^2.....\left(1\right)$ and

In $△ACO,A{C}^2=A{O}^2+O{C}^2.....\left(2\right)$

Subtracting equation 2 from 1, we get,

$A{B}^2-A{C}^2=A{O}^2-A{O}^2+B{O}^2-O{C}^2$

$\Rightarrow A{B}^2-A{C}^2=B{O}^2-O{C}^2$

$\Rightarrow 8^2-3^2=(BC+OC{)}^2-O{C}^2$

$\Rightarrow 55=(BC+OC{)}^2-O{C}^2$

$\Rightarrow 55=B{C}^2+O{C}^2+2BC\times OC-O{C}^2$

$\Rightarrow 55=6^2+2\times 6\times OC$

$\Rightarrow 55-36=12\times OC$

$\Rightarrow 12\times OC=19$

$\Rightarrow OC=19÷12=1.583\sim 1.6cm$