In a circle, points P, Q, R, and S lie on the circumference such that chords PR and QS intersect at the center, and both ∠RPQ and ∠RSQ are subtended by the same arc RQ. If ∠RPQ = 50°, what is the measure of ∠RSQ?
50°
Since PR and QS pass through the center, both are diameters, and P, Q, R, S all lie on the circle. Angles ∠RPQ and ∠RSQ are subtended by the same arc RQ from the same side, so \(\angle RSQ = \angle RPQ = 50°\).
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Important Questions from Circles, Chords and Tangents
In a circle, a ten cm long chord is at a distance of 12 cm from the centre of the circle. The length of the diameter of the circle (in cm) is:
Chord AB of a circle of radius 10 cm is at a distance 8 cm from the centre O. If tangents drawn at A and B intersect at P., then the length of the tangent AP (in cm) is:
A chord 21 cm long is drawn in a circle of diameter 25 cm. The perpendicular distance of the chord from the centre is:
In a circle with radius 5 cm, a chord is at a distance of 3 cm from the centre. The length of the chord is:
O is the centre of this circle. Tangent drawn from a point P, touches the circle at Q. If PQ = 24 cm and OQ = 10 cm, then what is the value of OP?
