मराठी

In Li.Pqr, Bisectors of Lpqr and Lprq Meet at I. Prove that I is Equidistant from the Three Sides of the Triangle 1 and Pi Bi Sects L Qpr . - Mathematics

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प्रश्न

In Δ PQR, bisectors of  ∠ PQR and ∠ PRQ meet at I. Prove that I is equidistant from the three sides of the triangle , and PI bisects ∠ QPR . 

आकृती
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उत्तर

Since I lies on bisector of  ∠ R, I is equidistant from PR and QR. 

Again I lies on the bisector of ∠ Q , I is equidistant from PQ and QR. 

Hence , I is equi distant from alI sides of the triangle. 

Therefore, I lies on the bisector of ∠ P i.e  ∠ QPR .

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पाठ 16: Loci - Exercise 16.1

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संबंधित प्रश्‍न

Construct a triangle ABC with AB = 5.5 cm, AC = 6 cm and ∠BAC = 105°

Hence:

1) Construct the locus of points equidistant from BA and BC

2) Construct the locus of points equidistant from B and C.

3) Mark the point which satisfies the above two loci as P. Measure and write the length of PC.


On a graph paper, draw the line x = 6. Now, on the same graph paper, draw the locus of the point which moves in such a way that its distantce from the given line is always equal to 3 units 


Ruler and compasses may be used in this question. All construction lines and arcs must be clearly shown and be of sufficient length and clarity to permit assessment.

  1. Construct a ΔABC, in which BC = 6 cm, AB = 9 cm and angle ABC = 60°.
  2. Construct the locus of all points inside triangle ABC, which are equidistant from B and C.
  3. Construct the locus of the vertices of the triangles with BC as base and which are equal in area to triangle ABC.
  4. Mark the point Q, in your construction, which would make ΔQBC equal in area to ΔABC, and isosceles.
  5. Measure and record the length of CQ.

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Use ruler and compass to answer this question. Construct ∠ABC = 90°, where AB = 6 cm, BC = 8 cm.

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