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If tangent PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 80°, then \(\angle PQA \) is equal to:
From a point T, the length of the tangent to a circle is 24 cm and the distance of T from the centre is 25 cm. The radius of the circle is :
Radius
At one end of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. The length of the chord, parallel to XY and at a distance of 8 cm from A is :
If angle between two radii of a circle is 130°, the angle between the tangents at the ends of the radii is :
Sum of the angles between the radius and between intersection point of tangent is , angle at the point of intersection of tangent
In the figure, AB is a chord of the circle and AOC is its diameter such that \(\angle ACB=50^o \). If AT is the tangent to the circle at the point A, then \(\angle BAT \) is equal to:
A tangent AB at a point A of a circle of radius 5 cm meets a line through the centre O at a point B so that OB = 12 cm. Length PB is :
The length of the tangent drawn from a point, whose distance from the centre of a circle is 20 cm and radius of the circle is 16 cm, is :
A tangent PQ at a point P of a circle of radius 15 cm meets a line through the centre O at a point Q so that OQ = 25 cm. Length of PQ is :
In a circle of radius 7 cm, tangent LM is drawn from a point L such that LM = 24 cm. If O is the centre of the circle, then length of OL is :
In the figure, PT is a tangent to a circle with centre O. If OT = 6 cm, and OP = 10 cm, then the length of tangent PT is :
In the given figure, O is the centre of two concentric circles of radii 3 cm and 5 cm. PQ is a chord of outer circle which touches the inner circle. The length of chord PQ is :
Length of chord
In the figure, TP and TQ are two tangents to a circle with centre O, so that \(\angle \)POQ = 140°. \(\angle \) PTQ is equal to:
In the figure, if TP and TQ are the two tangents to a circle with cent re O, so that \(\angle POQ=110^o \), then \(\angle PTQ \) is equal to:
In the figure, quadrilateral PQRS is circumscribed, touching the circle at A, B, C and D. If AP = 5 cm, QR = 7 cm and DR = 3 cm, then length PQ is equal to :
Length of the two tangents from a point to circle are equal
In the figure, if AD, AE and BC are tangents to the circle at D, E and F respectively, then:
( tangents from an external point of a circle are equal in length)
In the figure, the pair of tangents PA and PB drawn from an external point P to a circle with centre O are perpendicular to each other and length of each tangent is 5 cm. The radius of the circle is:
( tangent and radius are perpendicular at the point of contact)
From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. The area of the quadrilateral PQOR is:
Area of
Area of
Area of quadrilateral
In the figure, PQ is a chord of a circle and PT is the tangent at P such that \(\angle QPT=60^o \). Then \( \angle PRQ\) is equal to:
(radius)
In the figure, AT is a tangent to the circle with centre O such that OT = 4 cm and \(\angle \)OTA = 30°. Then AT is equal to :
Two circles touch each other externally at C and AB is a common tangent to the circles. \(\angle \)ACB is
Let
Similarly
In
PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such that \(\angle PQR=120^o.\ \angle OPQ \) is:
In the figure, PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and \(\angle BQR=70^o.\ \angle AQB \) is equal to
In the figure, PA and PB are tangents to the circle with centre O such that \(\angle APB=50^o.\ \angle OAB \) is equal to:
In the figure, O is the centre of the circle, PQ is a chord, and tangent PR at P makes and angle of 50° with PQ, then \(\angle \) POQ is equal to:
ABC is a triangle right angled at B with BC = 6 cm and AB = 8 cm. A circle with centre O and radius x cm has been inscribed in \(\triangle \) ABC as shown in the figure. The value of x is :