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प्रश्न
The bisectors of ∠B and ∠C of a quadrilateral ABCD intersect each other at point P. Show that P is equidistant from the opposite sides AB and CD.
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उत्तर
Since P lies on the bisector of angle B,
Therefore, P is equidistant from AB and BC ...(1)
Similarly, P lies on the bisector of angle C,
Therefore, P is equidistant from BC and CD ...(2)
From (1) and (2),
Hence, P is equidistant from AB and CD.
संबंधित प्रश्न
Use ruler and compasses only for this question.
- Construct ΔABC, where AB = 3.5 cm, BC = 6 cm and ∠ABC = 60°.
- Construct the locus of points inside the triangle which are equidistant from BA and BC.
- Construct the locus of points inside the triangle which are equidistant from B and C.
- Mark the point P which is equidistant from AB, BC and also equidistant from B and C. Measure and record the length of PB.
Describe the locus for questions 1 to 13 given below:
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Describe the locus of points at distances less than 3 cm from a given point.
Describe the locus of points at distances less than or equal to 2.5 cm from a given point.
Sketch and describe the locus of the vertices of all triangles with a given base and a given altitude.
In a quadrilateral PQRS, if the bisectors of ∠ SPQ and ∠ PQR meet at O, prove that O is equidistant from PS and QR.
Find the locus of points which are equidistant from three non-collinear points.
Show that the locus of the centres of all circles passing through two given points A and B, is the perpendicular bisector of the line segment AB.
