Question

Draw two lines AB, AC so that ∠ BAC = 40°:
(i) Construct the locus of the center of a circle that touches AB and has a radius of 3.5 cm.
(ii) Construct a circle of radius 35 cm, that touches both AB and AC, and whose center lies within the ∠ BAC.

Answer 1

Steps of Construction:
(i) Draw a line AX perpendicular to AB.
(ii) Mark off a point D on AX such that AD = 3.5 cm.
(iii) At D, draw the line DY at right angles to AX. Then DY is the required locus of the centre of circle that touches AB and has a radius of 3.5 cm.
(iv) Construct the bisector AZ of ∠ BAC intersecting DY at P.
(v) Draw PL, PM perpendicular to AB and AC respectively.
(vi) With P as centre and radius equal to 3.5, draw the circle which will pass through L and M.
Then this is the required circle that touches both AB and AC, and whose centre lies within the ∠ BAC.