Question

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

• A. $1\frac{7}{9}cm$
• B. $1\frac{7}{8}cm$
• C. $1\frac{7}{19}cm$
• D. $1\frac{7}{12}cm$

Answer 1

Answer: (D)

$1\frac{7}{12}cm$

In triangle AOB,
$A{B}^2=A{O}^2+O{B}^2$ (Pythagoras theorem)
$A{O}^2=A{B}^2-O{B}^2$ (I)
In triangle AOC,
$A{C}^2=O{C}^2+A{O}^2$ (Pythagoras theorem)
$A{O}^2=A{C}^2-O{C}^2$ (II)
From I and II,
$A{B}^2-O{B}^2=A{C}^2-O{C}^2$
$A{B}^2-(OC+BC{)}^2=A{C}^2-O{C}^2$
$8^2-(OC+6{)}^2=3^2-O{C}^2$
$64-O{C}^2-36-12OC=9-O{C}^2$
$12OC=19$
$OC=\frac{19}{12}$ = $1\frac{7}{12}$