In triangle $A B C$ , given below, $A B = 8 c m$ , $B C = 6 c m$ and $A C = 3 c m$ . Calculate the length of $O C$ .

2 c m

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3.32 c m

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1.58 c m

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1 c m

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Solution

The correct option is C $1.58 c m$
$I n △ A B O :$
$⟹ {A B}^{2} = {A O}^{2} + {B O}^{2}$
$⟹ 8^{2} = {A O}^{2} + {(6 + C O)}^{2}$
$⟹ {A O}^{2} + {(6 + C O)}^{2} = 64 - (1)$
$I n △ A C O$
$⟹ {A O}^{2} + {O C}^{2} = {A C}^{2}$
$⟹ {A O}^{2} = 9 - {C O}^{2} - (2)$
putting(2)in(1)
$⟹ 9 - {C O}^{2} + {(6 + C O)}^{2} = 64$
$⟹ 9 - {C O}^{2} + 36 + {C O}^{2} + 12 C O = 64$
$⟹ 45 + 12 C O = 64$
$⟹ 12 C O = 19$
$⟹ C O = \frac{19}{12} = 1.58 c m$

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

The correct option is C 1.58cmIn△ABO:⟹AB2=AO2+BO2⟹82=AO2+(6+CO)2⟹AO2+(6+CO)2=64−(1)In△ACO⟹AO2+OC2=AC2⟹AO2=9−CO2−(2) putting(2)in(1)⟹9−CO2+(6+CO)2=64⟹9−CO2+36+CO2+12CO=64⟹45+12CO=64⟹12CO=19⟹CO=1912=1.58cm

In triangle $A B C$ , given below, $A B = 8 c m$ , $B C = 6 c m$ and $A C = 3 c m$ . Calculate the length of $O C$ .