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.
Constructions
8 Likes
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.
Answered By
5 Likes
Related Questions
Using a ruler and compasses only :
(i) Construct a triangle ABC with the following data :
AB = 3.5 cm, BC = 6 cm and ∠ABC = 120°.
(ii) In same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC.
(iii) Measure ∠BCP.
Draw a line AB = 5 cm. Mark a point C on AB such that AC = 3 cm. Using a ruler and a compass only, construct :
(i) a circle of radius 2.5 cm, passing through A and C.
(ii) construct two tangents to the circle from the external point B. Measure and record the length of the tangents.
Draw two concentric circles with radii 4 cm and 6 cm. Taking a point on the outer circle, construct a pair of tangents to inner circle. By measuring the lengths of both the tangents, show that they are equal to each other.
Construct a triangle ABC in which AB = 5 cm, BC = 6.8 cm and median AD = 4.4 cm. Draw incircle of this triangle.