Mathematics
Construct a triangle ABC, with AB = 5.6 cm, AC = BC = 9.2 cm. Find the points equidistant from AB and AC; and also 2 cm from BC. Measure the distance between the two points obtained.
Answer
Steps of construction :
Draw a line segment AB = 5.6 cm
From A and B as centers and radius 9.2 cm, make two arcs which intersect each other at C.
Join CA and CB.
Draw two lines n and m parallel to BC at a distance of 2 cm.
Draw the angle bisector of ∠BAC which intersects n and m at points P and Q respectively.
On measuring PQ = 4.3 cm
Hence, P and Q are the required points which are equidistant from AB and AC; and also 2 cm from BC; PQ = 4.3 cm.
Related Questions
Draw an angle ABC = 75°. Find a point P such that P is at a distance of 2 cm from AB and 1.5 cm from BC.
A straight line AB is 8 cm long. Draw and describe the locus of a point which is :
(i) always 4 cm from the line AB.
(ii) 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.
Construct a triangle ABC, with AB = 6 cm, AC = BC = 9 cm. Find a point 4 cm from A and equidistant from B and C.
Draw a triangle ABC in which AB = 6 cm, BC = 4.5 cm and AC = 5 cm. Draw and label :
(i) the locus of the centers of all circles which touch AB and AC,
(ii) the locus of the centers of all the circles of radius 2 cm which touch AB.
Hence, construct the circle of radius 2 cm which touches AB and AC.