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Question
Construct an isosceles ∆ PQR such that PQ = PR = 6.5 cm and ∠PQR = 75°. Using a ruler and compasses only constructs a circumcircle to this triangle.
Solution
Steps of Construction :
(i) Draw a line segment PQ = 6.5 cm
(ii) At Q, draw a ray making an angle of 75°.
(iii) Through P, with a radius of 6.5 cm, draw an arc which intersects the angle ray at R.
(iv) Join PR,
Δ PQR is the required triangle.
(v) Draw the perpendicular bisectors of sides PQ and PR intersecting each other at O.
(vi) Join OP, OQ and OR.
(vii) With centre O and radius equal to OP or OQ or OR draw a circle which passes through P, Q and R. This is the required circumcircle of Δ PQR
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