Circles A and B are externally tangent. Angle PAB is a right angle. Segment PT is tangent to circle B at T. If the radius of circle A is 1 cm and the radius of circle B is 4 cm, what is the length of segment PT in cm?
+128474 Draw PB
Triangle PAB is right with AB = 5 and PA = 1 and PB the hypotenuse
So
sqrt [AB^2 + PA^2 ] = PB
sqrt [ 5^2 + 1^2 ] = PB
sqrt [26] = PB
And PBT is also a right triangle with PTB a right angle and TB = 4 and PB = sqrt (26) and PT a leg
So
sqrt [ PB^2 - TB^2 ] = PT
sqrt [ 26 - 4^2 ] = PT
sqrt [ 26 -16 ] = PT
sqrt [ 10 ] (cm) = PT
