The illustration shows two circles of radii 4 cm and 2 cm respectively. the distance between the two centre is 8 cm. find the length of the common tangent.
we know that ZY=4 cm AB=XY------> 2 cm ZX=ZY-XY------> 4-2----> 2 cm
in the right triangle AXZ applying the Pythagorean Theorem AZ²=AX²+XZ²-------> solve for AX AX²=AZ²-XZ²------> 8²-2²-----> AX²=60------> AX=√60-----> AX=2√15 cm BY=AX BY=2√15 cm-------> the length of the common tangent
the answer is the length of the common tangent is 2√15 cm
