CBSE Class 10 Circles Sure Shot Questions Set 03

Question. A point P is 7 cm from the centre of circle whose diameter is 8cm. How many tangents can be drawn to the circle ?
Answer: two

Question. Find the distance between two parallel tangents to a circle whose radius is 4.5 cm.
Answer: \( 9 \text{ cm} \)

Question. A square circumscribe a circle of radius 5 cm. Find the length of a diagonal of the square.
Answer: \( 10\sqrt{2} \text{ cm} \)

Question. Find the length of tangent drawn to a circle with radius 7 cm from a point 25 cm away from the centre of the circle.
Answer: \( 24 \text{ cm} \)

Question. A point P is 26 cm away from the centre of a circle and the length of the tangent drawn from P to the circle is 24 cm. Find the radius of the circle.
Answer: \( 10 \text{ cm} \)

Question. If the length of a chord of a circle is 16 cm and is at a distance of 15 cm from the centre of the circle, then find the radius of the circle (in cm).
Answer: 17

Question. The radius of a circle is 6 cm. Then find the perpendicular distance from the centre of the circle to the chord which is 8 cm in length.
Answer: \( 2\sqrt{5} \text{ cm} \)

Question. In a circle with centre O, AB and CD are two diameters perpendicular to each other. Then find the length of chord AC.
Answer: \( \frac{1}{\sqrt{2}} AB \)

Question. In a circle with centre O, the unequal chords AB and CD intersect each other at P. Then find, \( \Delta APC \) and \( \Delta DPB \).
Answer: Similar

Question. Two equal circles of radius r intersect such that each passes through the centre of the other. Then find the length of common chord.
Answer: \( r\sqrt{3} \)

Question. If four sides of a quadrilateral ABCD are tangential to a circle, then find relation between AB, BC, CD, AD, BD.
Answer: AB + CD = BC + AD

Question. Find the length of the tangent drawn from a point 8 cm away from the centre of a circle of radius 6 cm.
Answer: \( 10 \text{ cm} \)

Question. Two circles of radii 20 cm and 37 cm intersect in A and B. If O and O' are their centres and AB = 24 cm, then find distance OO'.
Answer: \( 51 \text{ cm} \)

Question. If two diameters of a circle intersect each other at right angles, then find the type of quadrilateral formed by joining their end points.
Answer: square

Question. If ABC is an arc of a circle and \( \angle ABC = 135^\circ \), then find the ratio of arc PQR to the circumference.
Answer: 3 : 8

Question. If one angle of a cyclic trapezium is triple the other, then find the greater one measures.
Answer: \( 135^\circ \)

Question. Find the angle in a major segment of a circle.
Answer: Less than \( 90^\circ \)

Question. AB and CD are two parallel chords of a circle with centre O such that AB = 6 cm and CD = 12 cm. The chords are on the same side of the centre and the distance between them is 3 cm. Then find the radius of the circle.
Answer: \( 3\sqrt{5} \text{ cm} \)

Question. In a circle of radius 17 cm, two parallel chords are drawn on opposite side of a diameter. The distance between the chords is 23 cm. if the length of one chord is 16 cm. Then find the length of the other.
Answer: \( 30 \text{ cm} \)

Question. If two circle are such that the centre of one lies on the circumference of the other, then find the ratio of the common chord of the two circles to the radius of any one of the circles.
Answer: \( \sqrt{3} : 1 \)

Question. If tangents QR, RP, PQ are drawn respectively at A, B, C to a circle circumscribing an acute angled \( \Delta ABC \) so as to form another \( \Delta PQR \), then find \( \angle RPQ \).
Answer: \( 180^\circ - 2 \angle BAC \)

Question. Two circles touch externally. The sum of their areas is \( 130 \pi \) sq cm and the distance between their centres is 14 cm. Find the radius of the smaller circle.
Answer: \( 3 \text{ cm} \)

Question. Two circles touch internally. The sum of their areas is, \( 116 \pi \) sq. cm and the distance between their centres is 6 cm. Find the radius of the larger circle.
Answer: \( 10 \text{ cm} \)

Question. Two circles touch each other internally. Their radii are 2 cm and 3 cm. Find the biggest chord of the outer circle which is outside the inner circle, is of length.
Answer: \( 4\sqrt{2} \text{ cm} \)