A tangent PQ at a point P of a circle of radius 5 cm meets a line through the center O at a point Q such that PQ = 12 cm. Find the length of OQ.
Find the radius of a circle, if the length of the tangent from a point at a distance of 25 cm from the center of the circle, is 24 cm.
If PQ is a tangent to a circle with center O and radius 6cm such that , then find the length of a tangent PQ and a line OQ.
If AB is a tangent drawn from a point A to a circle with center O and BOC is a diameter of the circle such that , then find
(i) In the given figure, find the value of .
(ii) from the given figure, find the value of
Find the length of tangent to a circle from a point at a distance of 5 cm from the centre of the circle of radius 3 cm.
IF O is the center of a circle. PQ is chord and the tangent PR at P makes an angle of with PQ, then find
In the given figure, XP and XQ are tangents from X to the circle with O. R is a point on the circle.
Prove that XA + AR = XB + BR.
O is the center of a circle of radius 5 cm. T is a point such that OT = 13 cm and OT intersects the circle at E. If AB is the tangent to the circle at E, then find the length of AB.
Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.
If the radius of a circle is 5 cm. then find the distance between two parallel tangents.
In the adjoining figure, a circle touches all the four sides of a quadrilateral ABCD whose three sides are AB = 6 cm, BC = 7 cm, and CD = 4cm. Find the length of AD.
In the given figure, O is the centre of two concentric circles of radii 4 cm and 6 cm, respectively. PA and PB are tangents to the outer and inner circles, respectively. If PA = 10 cm, then find the length of PB up to one place Of decimal.
ABCD is a quadrilateral such that A circle C (O, r) touches the sides AB, BC, CD, and DA at P, Q, R, and S, respectively. If BC = 38 cm, CD = 25 cm and BP = 27 cm. then find the value of r.
In the given figure, PA and PB are tangents to the given circle such that PA = 5 cm and Find the length of chord AB.
how many tangents can a circle have?
Fill in the blanks.
(i) A tangent to a circle intersects it in ____________ point(s).
(ii) A line intersecting a circle in two points is called a ______________.
(iii) A circle can have ____________ parallel tangenst at the most.
(iv) The common point of a tangent to a circle and the circle is called ______________.
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 = 12 cm. Length of PQ is
1. 12 cm
2. 13 cm
3. 8.5 cm
Draw a circle and two lines parallel to a given line such that one is a tangent and the other a. secant to the circle.
In the given figure, if TP and TQ are the two tangents to a circle with center O, so that
Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.
7 Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.
In the given figure, XY and X'Y' are two parallel tangents to a circle with center O and another tangent AB with the point of contact C intersecting XY at A and X'Y' at B. Prove that
Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.
Prove that the parallelogram circumscribing a circle is a rhombus.
A ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm, respectively (see figure). Find the sides AB and AC.
Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the center of the circle.
How many tangents can be drawn to a circle from a point Plies outside the circle?
At which point a tangent is perpendicular to the radius?
What term will you use for a line which intersects a circle at two distinct points?
Write the name of the common point of the tangent to a circle and the circle.
What do you say about the line which is perpendicular to the radius of the circle through the point of contact?
Write the number of tangents to a circle that is parallel to a secant.
Find the distance between two parallel tangents of a circle of radius 3 cm.
If two tangents inclined at an angle of are drawn to a circle of radius 3 cm, then find the length of each tangent.
In the given figure, AB, AC, and PQ are tangents. If AB = 5 cm, then find the perimeter of
Two concentric circles with centre O are of radii 5 cm and 3 cm. From an external point P, two tangents PA and PB are drawn to these circles, respectively. If PA = 12 cm, then find the length of PB.
In two concentric circles, prove that all chords of the outer circle which touch the inner circle are of equal length.
If PA and PB are two tangents drawn from a point P to a circle with centre O touching it at A and B, prove that OP is the perpendicular bisector of AB.
In the adjoining figure, AD = 8 cm, AC = 6 cm, and TB is the tangent at B to the circle with center O. Find OT, if BTis 4 cm.
The tangents drawn at the endpoints of two perpendicular diameters Of a circle are parallel to each other, which form of a square and whose length of the side is 2 cm. Find the radius of the circle.
In the given figure, common tangents AB and CD to two circles intersect at E. Prove that AB = CD.
In the adjoining figure, from an external point P, two tangents PT and PS are drawn to a circle with center O and radius r. If OP = 2r, then show that
At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. Find the length Of the chord CD parallel to XY and at a distance 8 cm from A.
The radii of two concentric circles are 13 cm and 8 cm. ABis a diameter of the bigger circle. BD is a tangent to the smaller circle touching it at D. Find the length of AD.
A chord PQ of a circle is parallel to the tangent drawn at a point R Of the circle. Prove that R bisects the arc PRQ.
A circle is inscribed in a ABC having sides aB = 8 cm, BC = 10 cm, and CA = 12 cm as shown in figure. Find AD, BE, and CF.
If a hexagon ABCDEF circumscribe a circle, prove that AB + CD + EF = BC+DE + FA
If a, b, c are the sides of a right-angled triangle, where c is hypotenuse, then prove that the radius r of the circle which touches the sides of the triangle is given by .
In the given figure, AD is a diameter of a circle with center O and AB is a tangent at A. C is a point on the circle such that DC produced intersects the tangent at B and
PA and PB are the tangents to a circle which circumscribes an equilateral ABQ.
In the given figure, from an external point P, a tangent PT and a line segment PAB drawn to a circle with center O. ON is perpendicular to the chord AB. Prove that
As a part of a campaign, a huge balloon with a message of "AWARENESS OF CANCER" was displayed from the terrace of a tall building. It was held by strings of length 8 m each, which inclined at an angle of at the point, where it was tied as shown in the figure.
(i) the length of AB?
(ii) If the perpendicular distance from the center of the circle to the chord AB is 3 m, then find the radiUS of the circle.
(iii) Which method should be applied to find the radius of the circle?
(iv) What do you think of such a campaign?