Question

The length of arc AB is twice the length of arc BC of a circle with centre O. If $\angle$AOB is ${100}^o$ then $\angle$BOC is

• A. ${50}^o$
• B. ${60}^o$
• C. ${70}^o$
• D. ${55}^o$

Answer 1

The correct option is A

${50}^o$

Given

Arc AB : Arc BC = 2 : 1 (arc AB is twice arc BC)

$\Rightarrow$ $\angle$AOB : $\angle$BOC = 2 : 1 [equal arcs subtent equal angles at the centre]

Given $\angle$AOB = ${100}^o$

$\Rightarrow$ $\angle$BOC = 100 x $\frac{1}{2}$

= ${50}^o$