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Using Ruler and Compass Only, Construct a Triangle Abc Such that Ab = 5 Cm, Abc = 75°, and the Radius of the Circumcircle of Triangle Abc is 3.5 Cm. on the Same Diagram, Construct a Circle - Mathematics

Question

Using ruler and compass only, construct a triangle ABC such that AB = 5 cm, ABC = 75°, and the radius of the circumcircle of triangle ABC is 3.5 cm. On the same diagram, construct a circle, touching AB at its middle point and also touching the side AC.

Sum

Solution

Steps:
Draw a line segment AB = 5 cm long. Make an angle of 75° at 'B' draw perpendicular bisector of AB and the angular bisector of B.
Make 3.5 cm on the perpendicular bisector with O as centre and radius equal to OA or OB draw circumcircle. Mark 2.5 cm on AC from A. Join BD, it will intersect at P, with P as centre and PD as radius draw another circle.