Pythagoras Theorem Practice

A and B are the centers of two circles with radii 5 m and 4 m respectively. The illustrated common tangent has a length of 10 m. Find the distance between the centers.

The illustration shows two circles of radii 6 cm and 3 cm respectively. The distance between the two circles’ centers is 10 cm.

Find the length of the common tangent.

In the given figure, AB = 5 cm and AC = 13 cm.

Find the radius of the circle.

A tree is located in the corner of a rectangular field.

The field is 10 metres long and 9 metres wide.

The tree is 4 metres tall. Calculate the length AE.

An extension ladder rests against a vertical wall and reaches 6 m up the wall from the horizontal ground. When the ladder is extended a further 1 m, it reaches 2 m higher up the wall without its feet being moved from their original position. Find the original length of the ladder.