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Question
In the given figure, the radius of the circle is 4 cm and ∠POS = 90° . Find the length of QR.
In the given figure, the radius of the circle is 4 cm and ∠POS = 90° . Find the length of QR.
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Solution
Given: radius of the circle is 4 cm and ∠POS = 90°.
△POS is a right angled triangle [as, ∠POS = 90°]
OP = OS = 4 cm [radii of the same circle]
So, PS = √(4²+4²) = 4√2
∠POS = ∠QOR = 90° [vertically opposite angle]
So, by using the theorem which states that “If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.”
Therefore, Length of the chord PS = the length of the chord QR.
Since, PS = 4√2 cm
So, QR = 4√2 cm
Given: radius of the circle is 4 cm and ∠POS = 90°.
△POS is a right angled triangle [as, ∠POS = 90°]
OP = OS = 4 cm [radii of the same circle]
So, PS = √(4²+4²) = 4√2
∠POS = ∠QOR = 90° [vertically opposite angle]
So, by using the theorem which states that “If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.”
Therefore, Length of the chord PS = the length of the chord QR.
Since, PS = 4√2 cm
So, QR = 4√2 cm
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