Mathematics
Using a ruler and a compass construct a triangle ABC in which AB = 7 cm, ∠CAB = 60° and AC = 5 cm. Construct the locus of:
(i) Points equidistant from AB and AC.
(ii) Points equidistant from BA and BC.
Hence, construct a circle touching the three sides of the triangle internally.
Answer
Steps of construction :
Draw a line segment AB = 7 cm.
Construct AX such that ∠XAB = 60°.
With A as center and radius = 5 cm cut arc on AX and mark it as point C.
Join BC. ABC is the required triangle.
Draw AY and BZ, angle bisector of A and B.
Let AY and BZ meet at point O.
Draw OD ⊥ AB.
With O as center and OD as radius draw a circle.
(i) Hence, AY is the locus of points equidistant from AB and AC.
(ii) Hence, BZ is the locus of points equidistant from BA and BC.
Related Questions
Construct a triangle with sides 5 cm, 4 cm and 3 cm. Draw its circumcircle and measure its radius.
(ii) Using a ruler and a pair of compasses only, construct:
(a) a triangle ABC, given AB = 4 cm, BC = 6 cm and ∠ABC = 90°.
(b) a circle which passes through the points A, B and C and mark its centre as O.
Draw a right-angled ΔABC in which hypotenuse BC = 6.4 cm and the altitude from A on BC is 2.5 cm. Draw the circumcircle of the triangle and measure its radius.
Construct a ΔABC in which AB = 4.5 cm, BC = 7 cm and median AD = 4 cm. Draw the inscribed circle of the triangle and measure its radius.