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

$50^{o}$

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$60^{o}$

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$70^{o}$

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$55^{o}$

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Solution

The correct option is A
$50^{o}$

Given

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

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

Given $∠$ AOB = $100^{o}$

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

= $50^{o}$

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The length of arc AB is twice the length of arc BC of a circle with centre O. If ∠AOB is 100o then ∠BOC is

The correct option is A 50o Given Arc AB : Arc BC = 2 : 1 (arc AB is twice arc BC) ⇒ ∠AOB : ∠BOC = 2 : 1 [equal arcs subtent equal angles at the centre] Given ∠AOB = 100o ⇒ ∠BOC = 100 x 12 = 50o

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

The correct option is A
$50^{o}$

Given

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

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

Given $∠$ AOB = $100^{o}$

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

= $50^{o}$