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The Orthocentre

In Δ ABC, O...

Question

In $Δ A B C$ , O is the orthocentre and $∠ B O C = 2 ∠ A$ , then the measure of $∠ B O C$ is equal to:

120^{o}

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100^{o}

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80^{o}

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60^{o}

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Solution

The correct option is B $120^{o}$
In the case of Orthocenter
$∠ B O C + ∠ B A C = 180$ (Property)
$∠ B O C = 2 ∠ A$
$⟹ 2 ∠ A + A = 180$
$⟹ ∠ A = 60 °$
$∠ B O C = 2 ∠ A = 2 \times 60 = 120 °$

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