Question : 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?
Option 1: 26 cm
Option 2: 52 cm
Option 3: 13 cm
Option 4: 15 cm
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Correct Answer: 26 cm
Solution : Given, PQ is a tangent, PQ = 24 cm and OQ = 10 cm Since tangent is perpendicular to the radius at its point of contact, $\angle$OQP = 90$^\circ$ Using Pythagoras theorem, OP 2 = PQ 2 + OQ 2 ⇒ OP 2 = 24 2 + 10 2 ⇒ OP 2 = 676 ⇒ OP = 26 cm Hence, the correct answer is 26 cm.
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Question : If PT is a tangent at T to a circle whose centre is O and OP = 17 cm and OT = 8 cm, find the length of the tangent segment PT.
Question : Point O is the centre of a circle of radius 5 cm. At a distance of 13 cm from O, point P is taken. From this point, two tangents, PQ and PR, are drawn to the circle. Then, the area of quadrilateral PQOR is:
Question : The radius of a circle is 6 cm. The distance of a point lying outside the circle from the centre is 10 cm. The length of the tangent drawn from the outside point to the circle is:
Question : The chords PQ and RS of a circle, when produced, meet at a point O. If PQ = 6 cm, OQ = 8 cm, and OS = 7 cm, then the length (in cm) of the chord RS is:
Question : The length of the chord of a circle is 24 cm, and the perpendicular distance between the centre and the chord is 5 cm. The radius of the circle is:
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