What is the relation between BC and AD -A- BC - ADB- BC - ADC- BC -2 ADD- BC - AD

The correct option is A BC=AD Given: ∠ AOB=90^∘ ∠ COD=90^∘ Now, ∠ BOC=180 ∠ AOB=180^∘ 90^∘=90^∘ and ∠ AOD=180 ∠ COD=180^∘ 90^∘=90^∘ ⇒BC subtends 90^∘ at the ce ...

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Standard X

Mathematics

Length of an Arc

What is the r...

Question

What is the relation between $ˆ B C$ and $ˆ A D$ ?

$ˆ B C > ˆ A D$

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$ˆ B C < ˆ A D$

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$ˆ B C = ˆ A D$

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$ˆ B C = 2 ˆ A D$

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Solution

The correct option is C
$ˆ B C = ˆ A D$

Given: $∠ A O B = 90^{\circ}$

$∠ C O D = 90^{\circ}$

Now, $∠ B O C = 180 - ∠ A O B = 180^{\circ} - 90^{\circ} = 90^{\circ}$

and $∠ A O D = 180 - ∠ C O D = 180^{\circ} - 90^{\circ} = 90^{\circ}$

$\Rightarrow ˆ B C$ subtends $90^{\circ}$ at the centre and $ˆ A D$ also subtends $90^{\circ}$ at the centre.

We know that equal arcs subtends equal angles at the centre,

so, $ˆ B C = ˆ A D$

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What is the relation between ˆBC and ˆAD?

What is the relation between $ˆ B C$ and $ˆ A D$ ?