In Fig. 7, two equal circles, with centres O and O’, touch each other at X. OO’ produced meets the circle with centre O’ at A. - Mathematics

Advertisements
Advertisements

In Fig. 7, two equal circles, with centres 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. Find the value of `(DO')/(CO')`

Advertisements

Solution

AO’ = O’X = XO = OC …..(Since the two circles are equal.)

So, OA = AO’ + O’X + XO …..(A-O’-X-O)

∴ OA = 3O’A

In ΔAO'D and ΔAOC,

∠DAO'= ∠CAO ....(Common angle)

∠ADO'= ∠ACO ....(both measure 90°)

∴ ΔADO' ~ ΔACO ....(By AA test of similarity)

`:.(DO')/(CO')=(O'A)/(OA)=(O'A)/(3O'A)=1/3`

  Is there an error in this question or solution?
Chapter 8: Circles - Exercise 8 [Page 37]

APPEARS IN

RD Sharma Class 10 Maths
Chapter 8 Circles
Exercise 8 | Q 1 | Page 37

RELATED QUESTIONS

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 PQ is ______.


In the given figure O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC = 7.5 cm. Calculate the radius of a circle.


In the adjoining figure the radius of a circle with centre C is 6 cm, line AB is a tangent at A. Answer the following questions.
(1) What is the measure of ∠CAB ? Why ?
(2) What is the distance of point C from line AB? Why ?
(3) d(A,B) = 6 cm, find d(B,C).
(4) What is the measure of ∠ABC ? Why ? 


What is the distance between two parallel tangents of a circle having radius 4.5 cm ? Justify your answer.


Four alternative answers for the following question is given. Choose the correct alternative.
 If two circles are touching externally, how many common tangents of them can be drawn?


How many common tangents can be drawn to two circles, touching each
other externally?


In the figure, point Q is the
point of contact. If PQ = 12,
PR = 8 then find PS.


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.


Two chords AB and CD of lengths 6cm and 12cm are drawn parallel inside the circle. If the distance between the chords of the circle is 3cm, find the radius of the circle.


In fig., PT is a tangent to the circle at T and PAB is a secant to the same circle. If PB = 9cm and AB = 5 cm, find PT.


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. 


A point A is 17cm from the centre of the circle. The length of the tangent drawn from A to the circle is 15cm. find the radius of the circle.


In the figure, XP and XQ are tangents from X to the circle with centre O. R is a point on the circle. Prove that XA + AR = XB + BR. 


Construct a tangent to a circle with centre O and radius 3.5 cm at a point P on it. 


In the following figure, seg AB is a diameter of the circle, m (arc AKC) = 40°. Find the value of m (arc BMC).


Find the area of sector whose central angle and radius are 60o and 21 cm respectively.
`(pi = 22/7)`


In the following figure, seg AB is the diameter of the circle with center P. Line CB be the tangent and line AC intersects a circle in point D. Prove that:
AC x AD = 4 (radius)2


In Fig. the incircle of ΔABC touches the sides BC, CA, and AB at D, E respectively. Show that: AF + BD + CE = AE + BF + CD = `1/2`( Perimeter of ΔABC)


In the given figure, O is the centre of the circle. Tangents at A and B meet at C. If ∠ACO = 30°,
find: (i) ∠ BCO (ii) ∠ AOB (iii) ∠ APB


Draw a circle of radius 2.7 cm and draw a chord PQ of length 4.5 cm. Draw tangents at points P and Q without using centre.


In figure, M is the centre of the circle and seg KL is a tangent segment. If MK = 12, KL = `6sqrt(3)`, then find

(i) Radius of the circle.
(ii) Measures of ∠K and ∠M.


In figure, if ∠AOB = 125°, then ∠COD is equal to ______.


In the figure, if PA and PB are tangents to the circle with centre O such that ∠APB = 50°, then ∠OAB is equal to ______.


The distance between two parallel tangents of a circle of radius 4 cm is ______ 


In the following figure, PA and PB are tangents from a point P to a circle with centre O. Then the quadrilateral OAPB must be a ______ 


Find the value of ∠DCE.


In the given figure, PT is a tangent to the circle at T, chord BA is produced to meet the tangent at P. Perpendicular BC bisects the chord TA at C. If PA = 9 cm and TB = 7 cm, find the lengths of:

  1. AB
  2. PT


In the above figure, seg AB and seg AD are tangent segments drawn to a circle with centre C from exterior point A, then prove that: ∠A = `1/2` [m(arc BYD) - m(arc BXD)]


If two tangents TL and TM are drawn to a circle with centre C such that ∠LTM = 70°, then find ∠MCT.


A tangent JK is drawn to a circle with centre C such that CK = 6 cm and ∠CKJ = 60°. Find the length of the tangent JK.


In the given figure, XAY is a tangent to the circle centered at O. If ∠ABO = 40°, then find ∠BAY and ∠AOB.


The length of tangent drawn to a circle of radius 9 cm from a point 41 cm from the centre is ______.


Assertion (A): A tangent to a circle is perpendicular to the radius through the point of contact.

Reason (R): The lengths of tangents drawn from an external point to a circle are equal.


In the given figure O, is the centre of the circle. CE is a tangent to the circle at A. If ∠ABD = 26° find:

  1. ∠BDA
  2. ∠BAD
  3. ∠CAD
  4. ∠ODB


Share
Notifications



      Forgot password?
Use app×