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 .

Advertisements
Advertisements

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
Advertisements

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 .

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 15: Loci - Exercise 16.1

APPEARS IN

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Use ruler and compasses only for this question:

I. Construct  ABC, where AB = 3.5 cm, BC = 6 cm and ABC = 60o.
II. Construct the locus of points inside the triangle which are equidistant from BA and BC.
III. Construct the locus of points inside the triangle which are equidistant from B and C.
IV. Mark the point P which is equidistant from AB, BC and also equidistant from B and C. Measure and records the length of PB.


Describe the locus of a point P, so that:

AB2 = AP2 + BP2,

where A and B are two fixed points.


Use graph paper for this question. Take 2 cm = 1 unit on both the axes.

  1. Plot the points A(1, 1), B(5, 3) and C(2, 7).
  2. Construct the locus of points equidistant from A and B.
  3. Construct the locus of points equidistant from AB and AC.
  4. Locate the point P such that PA = PB and P is equidistant from AB and AC.
  5. Measure and record the length PA in cm. 

Construct an isosceles triangle ABC such that AB = 6 cm, BC = AC = 4 cm. Bisect ∠C internally and mark a point P on this bisector such that CP = 5 cm. Find the points Q and R which are 5 cm from P and also 5 cm from the line AB. 


In the given figure ABC is a triangle. CP bisects angle ACB and MN is perpendicular bisector of BC. MN cuts CP at Q. Prove Q is equidistant from B and C, and also that Q is equidistant from BC and AC. 


In given figure, ABCD is a kite. AB = AD and BC =CD. Prove that the diagona AC is the perpendirular bisector of the diagonal BD. 


Draw and describe the lorus in  the following cases: 

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


Using only ruler and compasses, construct a triangle ABC 1 with AB = 5 cm, BC = 3.5 cm and AC= 4 cm. Mark a point P, which is equidistant from AB, BC and also from Band C. Measure the length of PB. 


State and draw the locus of a point equidistant from two given parallel lines.


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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×