Mathematics
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.
Answer
Steps of construction :
Draw BC = 7.2 cm.
Draw a ray BX, such that ∠XBC = 90°.
With B as center and radius = 6 cm cut an arc on BX and mark point A.
Join AC.
Take a point D on AC such that BD ⊥ AC.
Draw perpendicular bisectors of BD and BC which intersect at I.
With I as center and IC as radius draw a circle passing through B, D and C. Measure IC.
Hence, above is the required circumcircle with radius = 3.6 cm.
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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.
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.