Mathematics
Construct a triangle ABC with ∠ABC = 60°, AB = 6 cm and BC = 5 cm. Extend side AB to a point D so that AD = 9 cm. Also, extend side AC to a point E so that AE = 8 cm. Construct a circle which must touch AB produced, BC and AC produced.
Answer
Steps of Construction
Draw a line segment AB = 6 cm.
At point B, construct an angle of 60° with BA.
On this ray, mark point C such that BC = 5 cm.
Join AC. Thus, △ABC is constructed.
Produce AB beyond B. On the produced line, mark point D such that AD = 9 cm.
Produce AC beyond C. On the produced line, mark point E such that AE = 8 cm.
Since the required circle touches AB produced, BC, and AC produced, it is the excircle opposite vertex A.
Draw the external angle bisectors of ∠B and ∠C. Let them intersect at point O.
From O, draw a perpendicular to BC, meeting BC at P.
With centre O and radius OP, draw a circle. The circle so obtained touches AB produced, BC, and AC produced.
Related Questions
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In triangle ABC, ∠ABC = 90°, side AB = 6 cm, side BC = 7.2 cm and BD is perpendicular to side AC. Draw circumcircle of triangle BDC and then state the length of the radius of this circumcircle drawn.
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.