English

Describe the locus of the centres of all circles passing through two fixed points. - Mathematics

Advertisements
Advertisements

Questions

Describe the locus of the centres of all circles passing through two fixed points. 

Draw and describe the locus in the following case:

The locus of centres of all circles passing through two fixed points.

Diagram
Short Answer
Advertisements

Solution

The locus of the centre of all the circles which pass through two fixed points will be the perpendicular bisector of the line segment joining the two fixed points which are given.

shaalaa.com
  Is there an error in this question or solution?
Chapter 14: Locus - Exercise 14 [Page 302]

APPEARS IN

Nootan Mathematics [English] Class 10 ICSE
Chapter 14 Locus
Exercise 14 | Q 2. (iv) | Page 302

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Use ruler and compasses only for this question.

  1. Construct ΔABC, where AB = 3.5 cm, BC = 6 cm and ∠ABC = 60°.
  2. Construct the locus of points inside the triangle which are equidistant from BA and BC.
  3. Construct the locus of points inside the triangle which are equidistant from B and C.
  4. Mark the point P which is equidistant from AB, BC and also equidistant from B and C. Measure and record the length of PB.

The given figure shows a triangle ABC in which AD bisects angle BAC. EG is perpendicular bisector of side AB which intersects AD at point F.

Prove that: 


F is equidistant from AB and AC.


In the given triangle ABC, find a point P equidistant from AB and AC; and also equidistant from B and C. 

 


Describe the locus of a point in rhombus ABCD, so that it is equidistant from

  1. AB and BC;
  2. B and D.

The speed of sound is 332 metres per second. A gun is fired. Describe the locus of all the people on the earth’s surface, who hear the sound exactly one second later.


A straight line AB is 8 cm long. Draw and describe the locus of a point which is:

  1. always 4 cm from the line AB.
  2. equidistant from A and B.
    Mark the two points X and Y, which are 4 cm from AB and equidistant from A and B. Describe the figure AXBY.

In a quadrilateral ABCD, if the perpendicular bisectors of AB and AD meet at P, then prove that BP = DP. 


In Fig. ABCD is a quadrilateral in which AB = BC. E is the point of intersection of the right bisectors of AD and CD. Prove that BE bisects ∠ABC.


ΔPBC and ΔQBC are two isosceles triangles on the same base BC but on the opposite sides of line BC. Show that PQ bisects BC at right angles.


Use ruler and compasses for the following question taking a scale of 10 m = 1 cm. A park in a city is bounded by straight fences AB, BC, CD and DA. Given that AB = 50 m, BC = 63 m, ∠ABC = 75°. D is a point equidistant from the fences AB and BC. If ∠BAD = 90°, construct the outline of the park ABCD. Also locate a point P on the line BD for the flag post which is equidistant from the corners of the park A and B.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×