Construct any acute angled $△$ PQR. Find a point in its interior which is equidistant from points P,Q and R. Use compass, justify your construction.

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Steps of construction :

$(i) Draw an acute traingle △ PQR . (iI) Draw the perpendicular bisectors of sides PQ, QR and PR . (iii) Let them intersect at O in the interior of △ PQR . (iv) Name the points A, B and C where perpendicular bisectors intersect the sides . (v) Measure OA, OB and OC . We observe that OA = OB = OC Justification : By perpendicular - bisector theorem, O is equidistant from P, Q and R . Thus, OA = OB = OC .$

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Construct any acute angled △PQR. Find a point in its interior which is equidistant from points P,Q and R. Use compass, justify your construction.

Construct any acute angled $△$ PQR. Find a point in its interior which is equidistant from points P,Q and R. Use compass, justify your construction.