Class 10 Circles Previous Year Questions
Q1:
In the given figure, tangents PQ and PR are drawn to a circle such that ∠RPQ = 30°. A chord RS is drawn parallel to the tangent PQ. Find the measure of ∠RQS.
CBSE [2023]
EasyQ2:
A circle touches the side BC of a ∆ABC at a point P and touches AB and AC when produced at Q and R respectively. Show that AQ = \(\frac{1}{2}\) × perimeter of ∆ABC
CBSE [2023]
MediumQ3:
In the given figure, PA and PB are tangents from external point P to a circle with centre C and Q is any point on the circle. Then the measure of ∠AQB is:
CBSE [2023]
EasyQ4:
In the given figure, PQ is a chord of the circle centred at O. PT is a tangent to the circle at P. If ∠QPT = 55°, then find ∠PRQ.
CBSE [2023]
EasyQ5:
Two circles with centres O and O' of radii 6cm and 8cm, respectively intersect at two points P and Q such that OP and O'P are tangents to the two circles. Find the length of the common chord PQ.
CBSE [2023]
HardQ6:
In the given figure, PT is a tangent to the circle centred at O. OC is perpendicular to chord AB. Prove that PA.PB = PC² - AC².
CBSE [2023]
EasyQ7:
In the given figure, AC and AB are tangents to a circle centred at O. If ∠COD = 120°, then ∠BAO is equal to:
CBSE [2023]
EasyQ8:
In the given figure, TA is a tangent to the circle with centre O such that OT = 4cm, ∠OTA = 30°, then length of TA is:
CBSE [2023]
EasyQ9:
In the given figure, O is the centre of the circle and QPR is a tangent to it at P. Prove that ∠QAP + ∠APR = 90°.
CBSE [2023]
MediumQ10:
In the given figure, PQ is tangent to the circle centred at O. If ∠AOB = 95°, then find the measure of ∠ABQ
CBSE [2023]
EasyQ11:
In the given figure, a circle is inscribed in a quadrilateral ABCD in which ∠B = 90°. If AD = 17cm, AB = 20cm and DS = 3cm, then find the radius of the circle.
CBSE [2023]
EasyQ12:
Two tangents TP and TP are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2∠OPQ.
CBSE [2023]
EasyQ13:
In fig, there are two concentric circles with centre O. If ARC and AQB are tangents to the smaller circle from the point A lying on the larger circle, find the length of AC, if AQ = 5cm.
CBSE [2022]
EasyQ14:
In fig, O is the centre of a circle of radius 5cm. PA and BC are tangents to the circle at A and B respectively. If OP = 13cm, then find the length of tangents PA and BC.
CBSE [2022]
MediumQ15:
In fig, two circles with centres at O and O' of radii 2r and r respectively, touch each other internally at A. A chord AB of the bigger circle meets the smaller circle at C. Show that C bisects AB.
CBSE [2022]
MediumQ16:
In fig, PQ and PR are tangents to the circle centered at O. If ∠OPR = 45°, then prove that ORPQ is a square.
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MediumQ17:
In fig, PQ is a chord of length 8cm of a circle of radius 5cm. The tangents at P and Q meet at a point. Find the length of TP.
CBSE [2022]
HardQ18:
In fig, XAY is a tangent to the circle centered at O. If ∠ABO = 40°, then find ∠BAY and ∠AOB.
CBSE [2022]
MediumQ19:
In fig, AB is diameter of a circle centered at O. BC is tangent to the circle at B. If OP bisects the chord AD and ∠AOP = 60°, then find ∠C.
CBSE [2022]
MediumQ20:
In fig, a right triangle ABC in which ∠B = 90°, AB = 12cm and BC = 5cm is shown. Find the radius of the circle inscribed in the triangle ABC.
CBSE [2022]
MediumQ21:
In fig, a triangle ABC with ∠B = 90° is shown. Taking AB as diameter, a circle has been drawn intersecting AC at point P. Prove that the tangent drawn at point P bisects BC.
CBSE [2022]
HardQ22:
