Properties of Triangles

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length \(x\). The maximum area enclosed by the park is

ABC is a triangle, G is the centroid, D is the mid-point of BC. If A = (2, 3) and G = (7, 5), then the point D is

ABC is a triangle with \(\angle A=30^\circ\) and BC = 10 cm. The area of the circumcircle of the triangle is

The orthocentre of the triangle with vertices A(0, 0), B(0, 3/2), C(\(-\)5, 0) is