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In Given Figure 1 Abcd is an Arrowhead. Ab = Ad and Bc = Cd. Prove Th at Ac Produced Bisects Bd at Right Angles at the Point M. - Mathematics

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प्रश्न

In given figure 1 ABCD is an arrowhead. AB = AD and BC = CD. Prove th at AC produced bisects BD at right angles at the point M

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उत्तर

A is equidistant from B and 0 . Therefore, A lies on perpendicular bisector of BO. 

C is equidistant from Band 0. Therefore, C lies on perpendicular bisector of BO. 

A and C both lie on perpendicular bisector of BO. 

Hence, AC is perpendicular bisector of BO. 

Since AC is perpendicular bisector of BO so ∠ AMB = ∠ AMO = right angle.

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पाठ 16: Loci - Exercise 16.1

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संबंधित प्रश्‍न

Describe the locus of a point P, so that:

AB2 = AP2 + BP2,

where A and B are two fixed points.


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The locus of points at a distance of 4 cm from a fixed line. 


Describe completely the locus of a point in the following case:

Centre of a ball, rolling along a straight line on a level floor. 


Without using set squares or protractor construct a triangle ABC in which AB = 4 cm, BC = 5 cm and ∠ABC = 120°.
(i) Locate the point P such that ∠BAp = 90° and BP = CP.
(ii) Measure the length of BP.


Using only a ruler and compass construct ∠ABC = 120°, where AB = BC = 5 cm.
(i) Mark two points D and E which satisfy the condition that they are equidistant from both ABA and BC.
(ii) In the above figure, join AD, DC, AE and EC. Describe the figures:
(a) AECB, (b) ABD, (c) ABE.


Without using set squares or a protractor, construct:

  1. Triangle ABC, in which AB = 5.5 cm, BC = 3.2 cm and CA = 4.8 cm.
  2. Draw the locus of a point which moves so that it is always 2.5 cm from B.
  3. Draw the locus of a point which moves so that it is equidistant from the sides BC and CA.
  4. Mark the point of intersection of the loci with the letter P and measure PC.

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