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Syllabus

A triangle 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 given figure). Find the sides AB and AC.

explain this some in a little easy maNNER.PLS EXPERTSS

M and N are the centres of two circles of radii 7cm and 4cm respectively the direct common tangent to the circle meet MN at P then in what ratio does P divide MN

prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

ABC is a right triangle right angled at B, such that BC = 6 cm and AB = 8 CM, find the radius of its in circle.

one circle has radius 5 and its centre (0,5). A second circle has radius of 12 and its centre (12,0). What is the length of the radius of a third circle which passes through the centre of the second circle and both the points of intersection of the first two circles.

PQ is a chord of length 8cm of a circle of radius 5cm. The tangent at P and Q intersect at a point T. Find the length TP?

CAN I GET THE CORRECT EXPLATION OF THIS EXAMPLE????

plz

PT to the circle and a line PB intersect

ing the circle at two points A and B are

drawn. If PA =8 cm, and PT = 12 cm

then length of PB is

prove that the tangent drawn at the mid point of an arc of a circle is parallel to the chord joining the end points of the arc

Two circles touch each other at point C. Prove that the common tangent to the circles at C, bisects the common tangent P & Q.

A circle touches the side Bc of a triangle ABC at a point P and touches AB and AC when produced at Q and R respectively. Show that

From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP is equal to the diameter of the circle, show that triangle APB is equilateral.

prove that the length of the tangents drawn from an external point to a circle are equal, hence show that the centre lies on the bisector of the angle between the two tangents?

ab is a chord of length 16cm of a circle of radius 10 cm .the tangents at a and b intersect at point p.find the length of pa

A semi circle is drawn outwardly on chord AB of a cirle with centre O and unit radius. The perpendicular from O to AB, meets the seme circle on AB at C. Determine the measure of angle AOB and lenhtg AB s that Oc has max. length.

Two tangents TP and TQ are drawn to a circle with center O from an external point T. Prove that angle PTQ = 2 OPQ.

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.

Ab is a diameter and AC is a chord of a circle such that angle BAC =30 .If then tangent at C intersects AB produced in D,prove that BC=BD

If the angle between two radii of a circle is 140 DEGREE, then the angle between the tangets at the ends of the radii is ?

If an isosceles triangle ABC in which AB = AC = 6 cm is inscribed in a

(A) PQ = 13 cm

(B) PQ = 10 cm

(C) RS = 13 cm

(D) area of trapezium RSCD is 78 $c{m}^{2}$

A chord of circle of radius 10 cm subtends a right angle at the centre.Find the area of the corresponding minor segment and hence find the area of the major sector?

The radii of two concentric circles are 13 cm and 8 cm . AB is a diameter of the bigger circle BD is tangent to the smaller circle touching it at D.Find the length of AD

If a, b, c are the sides of a right triangle where c is the hypotenuse, then prove that radius r of the circle touches the sides of the triangle is given by r = a+b+c/2

Two tangent segments PA and PB are drawn to a circle with centre O, such that angle APB= 120degree. Prove that OP=2AP.

IF ANGLE BETWEEN TWO TANGENTS DRAWN FROM A POINT P TO A CIRCLE OF RADIUS A AND CENTER O IS 60 DEGREE THEN PROVE THAT AP = A UNDER ROOT 3.

In solution it's given TO is the angle bisector of anglePTQ and TO perpendicular to PQ.

PLEASE EXPLAIN HOW

ASAP.

prove that the tangents drawn at ends of a diameter of a circle are parallel.

two chords PQ and RS intersect at T outside the circle.if PQ =5cm OT =3cm TS =2cm length of RS is

From an external point P, two tangents PA and PB are drawn to a circle

Prove that the parallelogram circumscribing a circle is a rhombus. in this question do also have to prove that the diagonals are also equal?

two circles with centres O and O' of radii 3cm and 4cm respectively intersect at two points P and Q such that OP and O'P are tangents to the two circles find the lenghth of the common chord PQ.

r) is produced to P so that BP = 2 AB.Prove that: OP

^{2}= OA^{2}+ 6 AB^{2}.A circle touches all the four sides of a quadrilateral ABCD whose sides are AB = 6 cm , BC = 7 cm and CD = 4 cm. Find AD.

A circle is inscribed in a triangle ABC, having sides 8 cm , 10 cm and 12 cm. Find AD , BE and CF ( these 3 are altitudes of triangle ABC).

if from any point on the common chord of two intersecting circles , tangents be drawn to the circles , prove that they are equal .

If PA and PB are tangents from an outside point P. Such that PA = 10cm and ∠APB = 60°. Find the length of cord AB.PQ and RS are two parallel tangents to a circle with centre'O',another tangent AB with the point of contact 'C' intersecting PQ and RS at A and B respectively.Prove that angle AOB=90 degree.

If a, b and c are are the sides of a right triangle, where c is the hypotenuse, then show that radius of the incircle r is equal to (a+b-c)/2.

[1]If PA and PB are tangents from an outside point P such that PA = 10 cm and angle APB = 60 .find the length of the chord AB.

[2]prove that the tangent drawn at the ends of a chord of a circle make equal with the chord.

[3]prove that the line segment joining the points of contact of two parallel tangent to a circle is a diameter of the circle.

" The tangent to a circle is a special case of the secant when the two end points of its corresponding chord coincide" can someone please explain what does this means ????

The radius of the incircle of a triangle is 4 cm and the segments into which one side is divided by the point of contact are 6cm and 8 cm .Determine the other two sides of the triangle.a triangle ABC is drawn to circumscribe a circle. if AB = 13cm , BC= 14cm and AE= 7CM then AC is equal to what ?

Two circles touch externally at a point P and a common tangent touches them at A and B.Prove that AB subtends a right angle at P.

Prove that the direct common tangent to two circles touching each other externally subtends a right angle at the point of contact.Tangents PQ and PR are drawn to a circle such that angle RPQ= 30 degreeA chord RS is drawn parallel to tangent PQ.

Find angle RQS...??? ANSFAST...

Prove that the line segment joining the points of contact of two parallel tangents passes through center of circle .

ab and cd are common tangents to two circles of unequal radii. prove that ab=cd

From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP = diameter of the circle, show that the triangle APB is equilateral.

In a right triangle ABC in which angle B = 90', a circle is drawn with AB as diameter intersecting the hypotenuse ACat P. Prove that the tangent to the circle at P visects BC.

(A) 13 cm

(B) 15 cm

(C) 11 cm

(D) 10 cm

prove that the parallelogram circumscribing a circle is a rhombus.???

PAB is a secant and PT is a tangent. Prove that PA X PB =PT^{2}oabc is a rhombus whose 3 vertices a.b and c lie on the circle with centre o. if thre radius of the circle is 10 cm , find the area of the rhombus

the difference of squares of two numbers is 180. the square of smaller no. is 8 times the larger number. find the two numbers .

The sides AB,BC,CA of triangle ABC touch a circle with centre o and radius r at P,Q,R respectively.Prove that

(1) AB+CQ= AC+BQ

(2) Area (triangle ABC) = 1/2 (perimeter of triangle ABC) x r (radius)

Triangle ABC is isosceles in which AB=AC circumscribed about a circle. Prove that base is bisected by the point of contact.

in two concentric circles, prove that all chords of the outer circle which touches the inner circle are of equal lengths.

a) PAOB is a cyclic quadrilateral

b) PO is the bisector of angel APB

c) angel OAB = angel OPA

Equal circles with centres O and O' touch each other at X. OO' produced to meet a circle with centre O , at A. AC is a tangent to the circle whose centre is O. O'D is perpendicular to AC. Find the value of DO'/CO.....cAn aNy1 hElP MeH WiD thIs qUeStIoN pLs...???????

if PAB is a secant to a circle intersecting the circle at A and B and PT is a tangent segment, prove that

PA * PB=PT

^{2}Also, using the above theorem prove the following,

two circles intersect each other at P and Q. from a point R on PQ produced, two tangents RB and RC are drawn to the circles touching hem at B and C

prove tha RC=RB

If from a external point P of a circle with centre O, two tangents PQ and PRare drawn such that angle of QPR=120. prove tht 2PQ=PO.

The tangent at pt C of a circle and a diameter AB when extended intersect at P.If angle PCA = 110 find angle CBA

Three sides of a quadrilateral ABCD are AB=10cm. BC=7cm. CD=9cm. What can be the length of the fourth side, DA, if it can circumscribe a circle?

Ma'am I have rechecked the question.it is correct. Please help me out with the solution.

Q1) From an external point P, tangents PA and PB are drawn to a circle with cente O.If CD is the tangent to the circle at a point E and PA=14cm, find the perimeter of triangle PCD.

Q2) a circle touches all the four sides of a quadrilateral ABCD whose three sides are AB=6cm, BC=7cm, and CD=4cm find AD.

if possible u pls. explain me these sums through video.

PQ is tangent to outer circle and PR is tangent to inner circle. if PQ=4cm,OQ=3cm and OR=2cm then the length of PR is

a)5cm b)root21

c)4cm d)3cm

A boy is cycling such that the wheels of the cycle are making 140 revolutions per minute. If

(A) (2+√5)/2

(B) 5/2

(C) √5

(D) √6

prove that line segment joining the points of contact of two parallel tangents is the diameter of the circle

Prove that the angle between 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.

PQL and PRM are tangents to the circle with centre o at the points Q and R ,respectively and S is a point on the circle such that angle SQL=50 and angle SRM=60. Find angle QSR.

The tangent at a point C of a circle and diameter AB when extended intersect at P. If PCA=1100 , find CBA.6. The tangent at a point C of a circle and diameter AB when extended intersect at P. If PCA=1100 , find CBA.

ABCD is a quadrilateral such that angle D=90degree. A circle with centre O and radius r touches the sides AB,BC,CD and DA at P,Q,R and S respectively. If BC=38 cmCD=25cm and BP=27 cm find r