Mathematics
Using ruler and compasses only :
(i) Construct a triangle ABC with following data : AB = 3.5 cm, BC = 6 cm and ∠ABC = 120°.
(ii) In the same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle drawn which is equidistant from A and C.
Answer
Steps of construction :
Draw a line segment BC = 6 cm.
At point B, construct an angle of 120° with BC.
On the ray forming the angle, mark point A such that AB = 3.5 cm.
Join AC. Thus, △ABC is constructed.
To draw the circle with BC as diameter, construct the perpendicular bisector of BC.
Let the perpendicular bisector meet BC at O. Then O is the midpoint of BC.
With centre O and radius OB or OC, draw a circle. This is the required circle with BC as diameter.
Now, to find a point P on the circle which is equidistant from A and C, construct XY, the perpendicular bisector of AC.
Let XY, the perpendicular bisector of AC meet the circle at point P.
Then PA = PC, because every point on the perpendicular bisector of AC is equidistant from A and C.
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