Advertisements
Advertisements
Question
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.
Advertisements
Solution
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.
RELATED QUESTIONS
Draw an angle ABC = 75°. Draw the locus of all the points equidistant from AB and BC.
Describe the locus of the centre of a wheel of a bicycle going straight along a level road.
Describe the locus of points inside a circle and equidistant from two fixed points on the circumference of the circle.
Describe the locus of the centres of all circles passing through two fixed points.
Sketch and describe the locus of the vertices of all triangles with a given base and a given altitude.
In the given figure, obtain all the points equidistant from lines m and n; and 2.5 cm from O.
By actual drawing obtain the points equidistant from lines m and n; and 6 cm from a point P, where P is 2 cm above m, m is parallel to n and m is 6 cm above n.
A straight line AB is 8 cm long. Draw and describe the locus of a point which is:
- always 4 cm from the line AB.
- 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.
Find the locus of points which are equidistant from three non-collinear points.
In Fig. AB = AC, BD and CE are the bisectors of ∠ABC and ∠ACB respectively such that BD and CE intersect each other at O. AO produced meets BC at F. Prove that AF is the right bisector of BC.
