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Area of a Circle

In the given ...

Question

In the given figure, $Δ A B C$ is inscribed in a circle with centre O. If $Δ A C B = 65^{o}$ , find $∠ A B C$ .

25^{o}

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35^{o}

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Cannot be determined

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None of these

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Solution

The correct option is A $25^{o}$
$G i v e n - Δ A B C h a s b e e n i n s c r i b e d i n a c i r c l e w i t h c e n t r e O a n d d i a m e t e r B C . ∠ A C B = 90^{o} . T o f i n d o u t - ∠ A B C = ? S o l u t i o n - ∠ B A C = 90^{o} s i n c e i t i s a n a n g l e i n a s e m i c i r c l e . ∴ I n Δ A B C ∠ A C B + ∠ B A C + ∠ A B C = 180^{o} ⟹ ∠ A B C = 180^{o} - (∠ A C B + ∠ B A C) = 180^{o} - (65^{o} + 90^{o}) = 25^{o} . A n s - O p t i o n A .$

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In the given figure, ΔABC is inscribed in a circle with centre O. If ΔACB=65o, find ∠ABC.

The correct option is A 25oGiven−ΔABChasbeeninscribedinacirclewithcentreOanddiameterBC.∠ACB=90o.Tofindout−∠ABC=?Solution−∠BAC=90osinceitisanangleinasemicircle.∴InΔABC∠ACB+∠BAC+∠ABC=180o⟹∠ABC=180o−(∠ACB+∠BAC)=180o−(65o+90o)=25o.Ans−OptionA.

In the given figure, $Δ A B C$ is inscribed in a circle with centre O. If $Δ A C B = 65^{o}$ , find $∠ A B C$ .