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In the given figure, O is the centre of a circle. AB is a chord and AT is the tangent at A. If \(\angle AOB=100^o \), calculate \( \angle BAT\)
A chord of a circle of radius 10 cm subtends a right angle at its centre. The length of the chord is
In the given figure, PQ is a tangent at point C. If AB is a diameter and \(\angle CAB=30^o \). The value of \(\angle PCA \) is
(angle in the semicircle)
In
(Angle in the alternate segment)
In the given figure, AP, AQ and BC are tangents to the circle. If AB = 5 cm, AC = 6 cm, BC = 4 cm, the value of AP is
2 AP = Perimeter of triangle
AP
\(PQ \) and \(PR \) are two tangents to a circle with centre \(O \). If \(\angle QPR=46^o \) then the value of \(\angle QOR \) is
The sides AB, BC, CA of a triangle ABC touch a circle at P,Q,R respectively. If PA = 4 cm, BP = 3 cm, AC = 11 cm. The length of BC is
The perimeter of a square circumscribing a circle of radius \(a \) cm is
Perimeter
\(AB \) is the diameter of a circle with centre \(O \) and \(AT \) is a tangent. If \(\angle AOQ=58^o \), the value of \(\angle ATQ \) is
(Tangent is perpendicular to the radius)
Two concentric circles are of radius \(7\ cm\) and \(r\ cm \) respectively where \(r > 7\). A chord of the larger circle of length \(48\ cm \) touches the smaller circle. The value of \(r \) is
( Tangent is perpendicular to the radius)
In
A right triangle ABC circumscribes a circle of radius \(r \). If AB and AC are of length 8 cm and 6 cm respectively. The value of \(r \) is
Area of
Also
Area of
From a point Q, the length of the tangent to a circle is 24 cm and distance of Q from the centre is 25 cm. The radius of the circle is
Two concentric circles are of radius \(5\ cm\) and \(3\ cm \). Find the length of the chord of the larger circle which touches the smaller circle
From an external point P, tangents PA and PB are drawn to a circle with centre O. If \(\angle PAB=50^o \) then the value of \(\angle AOB \) is
( angle between radius and tangent is )
In
\(PQ \) is a tangent at a point \(C \) to a circle with centre \( O\). If \(AB \) is a diameter and \(\angle CAB=30^o \), the value of \( \angle PCA\) is
In
(radius)
( Angle opposite to equal sides are equal)
(Tangent is perpendicular to radius at point of contact)
From an external point P, two tangents PT and PS are drawn to a circle with centre O and radius r. If PO = 2r. The value of \(\angle \)OTS is
Let
In ,
In
(radius)
In
Two equal circles with centre O and O’ touch each other at X. OO’ produced meets the circle with centre O’ at A. AC is tangent to the circle with centre O at the point C. O’D is perpendicular to AC. The value of \(\mathrm{\dfrac{DO’}{CO}} \) is
(each )
(Common)
(AA centre)
\(PA \) and \(PB \) are tangents to the circle with centre O such that \(APB=50^o \). The value of \(\angle OAB \) is
( tangent is perpendicular to radius)
In
(radius)
Two concentric circle of radius \(a \) and \(b(b>a) \) are given. The length of the chord of the larger circle which touches the smaller circle is
In ,
O is the centre of a circle PT and PQ are tangent to the circle from an external point P. If \(\angle TPQ=70^o \). Find \(\angle TRQ \)
(Tangent is perpendicular to radius)
(Central angle is twice of inscribed angle)
Tangents PA and PB are drawn from an external point P to two concentric circles with centre O and radius 8 cm and 5 cm respectively. If AP = 15 cm the length of BP is
In
In
CP and CQ are tangents from an external point C to a circle with centre O. AB is another tangent which touches the circle at R. If CP = 11 cm, BR = 4 cm. The length of BC is
(Tangents drawn from an external point are equal)
(Tangent drawn from an external point are equal)
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 13 cm. The length of PQ is
ABCD is a cyclic quadrilateral. If \(\angle BAC=50^o \) and \(\angle DBC=60^o \). The value of \(\angle BCD \) is
(Angles in same segment)
In
The quadrilateral ABCD circumscribes a circle with centre O. If \(\angle AOB=115^o \) the value of \(\angle COD \) is
(V.O.A)
So,
O is the centre of a circle, PQ is a chord and the tangent PR at P makes an angle of \(50^o \) with PQ. The value of \(\angle \)POQ is
(radius)
PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of a circle such that \(\angle POR=120^o \). The value of \(\angle OPQ \) is
In the given figure, AB and AC are tangents to the circle with centre O such that \(\angle \)BAC = \( 40^o\). Then calculate \(\angle \)BOC
If angle between two tangents drawn from a point P to a circle of radius ‘a’ and centre O is \(90^o \), the value of OP is
So,
So, is a square
Two concentric circle of radius 6 cm and 4 cm with centre O are drawn. If AP is a tangent to the larger circle and BP the smaller circle and length of AP is 8 cm. The length of BP is
\(PQ \) is a tangent from an external point \(P \) to a circle with centre \(O \) and \(OP \) with the circle at \(T \) and \(QOR\) is a diameter. If \(\angle POR=130^o \) and \(S \) is a point on the circle. The value of \(\angle 1+\angle 2 \) is
( Central angle is twice of inscribed angle)
(linear pair)
If TP and TQ are two tangents to a circle with centre O, so that \(\angle \)POQ = \(110^o \), the value of \(\angle \)PTQ is
and
and
In quadrilateral we have
PA and PB are tangents from a point P to a circle with centre O. The quadrilateral OAPB is a
(Tangents and radius are perpendicular)
Which are opposite angles of quadrilateral
So, the sum of remaining two angles is also .
If \(PQR \) is a tangent to a circle at \(Q \) whose centre is \(O \), \(AB \) is a chord parallel to \(PR \) and \(\angle BQR=70^o \). The value of \(\angle AQB \) is
(alternate angles)
In and
(each )
( Common)
So, (CPCT)
\(PT \) touches the circle at \(R \) whose centre is \(O \). Diameter \(SQ \) when produced meets \(PT \) at \( P\). If \(\angle SPR=x^o \) and \(\angle QRP=y^o \). Then
(Same chord QR)
(angle in a semicircle is )
In
AB and PQ intersect at M. If A and B are centres of circles then
PQ is the common chord
AB bisects PQ at M so, PM = MQ
PQ is perpendicular to AB
PQ is tangent at a point R of the circle with centre O. If \(\angle \) TRQ = \(30^o \), the value of \(\angle \)PRS is
So,
(angles in a semicircle is )
A circle has \(\underline{\qquad} \) number of tangents
A circle has infinitely many tangents
If the angle between the two radius of a circle is \(120^o \), then the angle between the tangents at the end of the radius is
Angle between the tangents
If a parallelogram circumscribes a circle then it is a
In
Hence
So, and and
So,
So, is a rhombus as parallelogram with equal sides is a rhombus
If \(d_1,d_2\ (d_2>d_1) \) be the diameters of two concentric circles and C be the length of a chord of a circle which is tangent to the other circle then