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Question

Find the value of x.

$33^{o}$
$55^{o}$
$65^{o}$
None of these

A

55^{o}

B

33^{o}

C

65^{o}

D

None of these

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Solution

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If the tangent touches a circle at a point and a chord is drawn from the point of contact then angle made by that chord in the alternate segment of the circle is equal to the angle made by tangent to the circle. (Property)
Two chords are of equal length (as denoted in figure ) so angle made by them will be equal. (Property)
By the above mentioned properties both chord will make angle of $x$
And all three chords making a traingle in the circle so by triangle property $x + x + x + 15^{\circ} = 180^{\circ}$ (Because sum of all three internal angle of a traingle always equals to $180^{\circ}$ )
On solving further we get $x = 55^{\circ}$

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