Final answer:
To construct the circumcircle of triangle PQR, draw the perpendicular bisectors of two sides to find the center, measure the radius from the center to a vertex, and then draw the circle with this radius passing through all vertices.
Step-by-step explanation:
The problem involves drawing a triangle PQR with sides PQ = 5 cm, QR = 6.5 cm, and PR = 7 cm, and constructing its circumcircle. To do this, first sketch the triangle by accurately drawing the sides according to the given measurements. Then, find the perpendicular bisectors of at least two sides of the triangle (though all three can be done for accuracy). These should intersect at one point, which will be the center of the circumcircle. From this center, measure the distance to any vertex of the triangle (P, Q, or R); this will be the radius of the circumcircle. Finally, draw the circle with this radius, ensuring that it passes through all three vertices of triangle PQR. This circle is the circumcircle for triangle PQR.
Remember that the circumcircle of a triangle always passes through all three vertices, and its center is equidistant from them, found at the intersection of the perpendicular bisectors of the triangle's sides.