In following fig., PT is a tangent to the circle at $T$ and $PAB$ is a secant to the same circle. If $PB = 9\ cm$ and $AB = S\ cm$, find PT.
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Circles question types
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Sample Questions
Circles questions
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In following fig., $PT$ is a tangent to the circle at $T$ and $PAB$ is a secant to the same circle. If $PA =4 cm$ and $AB = Scm$, find $PT$ .
View full solution →In following fig., $PT$ is a tangent to the circle at $T$ and $PAB$ is a secant to the same circle. If $PA = 4cm$ and $AB = Scm,$ find $PT.$
View full solution →In a cyclic quadrilateral ABCD , AB || CD and ∠ B = 65 ° , find the remaining angles
In fig., O is the centre of the circle and $\angle AOC = 1500.$ Find $\angle ABC.$
View full solution →In following fig., PT is tangent to the circle at T and CD is a diameter of the same circle. If PC= 3cm and PT= 6cm, find the radius of the circle.
In following fig., chords PQ and RS of a circle intersect at T. If RS = 18cm, ST = 6cm and PT = 18cm, find the length of TQ.
In following fig., a circle is touching the side BC of Δ ABC at P and AB and AC produced at Q and R respectively. Prove that AQ is half the perimeter of Δ ABC.
In following figure , the incircle of Δ ABC , touches the sides BC , CA and AB at D , E and F respectively. Show AF + BD + CE = AE + BF + CD
PA and PB are tangents from P to the circle with centre O. At M, a tangent is drawn cutting PA at K and PB at N. Prove that KN = AK + BN.
In fig., AB and DC are two chords of a circle with centre O. these chords when produced meet at P. if PB = Bern, BA = 7cm and PO = 14.5cm, find the radius of the circle.
Bisectors of angles $A, B$ and $C$ of a triangle $A B C$ intersect its circumcircle at $D, E$ and $F$ respectively. Prove that the angles of $\triangle D E F$ are $90^{\circ}-\frac{ A }{2}, 90^{\circ}-\frac{ B }{2}$ and $90^{\circ}-\frac{ C }{2}$ respectively.
View full solution →Prove that the angles bisectors of the angles formed by producing opposite sides of a cyclic quadrilateral (provided they are not parallel) intersect at right triangle.
Two circles with centres O and P intersect each other at A and B as shown in following fig. Two straight lines MAN and RBQ are drawn parallel to OP.
Prove that (i) MN = 20 P (ii) MN= RQ.
Prove that (i) MN = 20 P (ii) MN= RQ.
Prove that the line segment joining the midpoints of two parallel chords of a circle passes through its centre.
In fig., chords AB and CD of a circle intersect at P. AP = 5cm, BP= 3cm and CP = 2.5cm. Determine the length of DP.
If Δ PQR is isosceles with PQ = PR and a circle with centre O and radius r is the incircle of the Δ PQR touching QR at T, prove that the point T bisects QR.
If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus.
From a point P outside a circle, with centre O. tangents PA and PB are drawn as following fig., Prove that ∠ AOP = ∠ BOP and OP is the perpendicular bisector of AB.
Two tangents are drawn to a circle from an external point P. touching the circle at the points A and B. A third tangent intersects segment PA in C and segment PB in D and touches the circle at Q. if PA = 20 units, find the perimeter of Δ PCD.
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