Question

The length of arcs AB and BC of a circle with centre O are in the ratio 3 : 2. If $\angle$AOB is ${96}^o$ then $\angle$BOC is

• A. ${64}^o$
• B. ${32}^o$
• C. ${128}^o$
• D. ${84}^o$

Answer 1

The correct option is A

${64}^o$

Given

Arc AB : Arc BC = 3 : 2

$\Rightarrow$ $\angle$AOB : $\angle$BOC = 3 : 2 [equal arcs subtent equal angles at the centre]

Given $\angle$AOB = ${96}^o$

$\Rightarrow$ $\angle$BOC = 96 x $\frac{2}{3}$

= ${64}^o$