Question

In the given figure, PT is tangent to the circle at T. If PA = 4 cm and AB = 5 cm, find PT. AB is equal to diameter.

Answer 1

Given that AB = 5 cm $\Rightarrow$ AO = 2.5 cm

PO = PA + AO = 4 + 2.5 cm

PO = 6.5 cm

Applying Pythagoras theorem to $△$OTP

${PT}^2$ = ${OP}^2$ - ${OT}^2$

${PT}^2$ = ${6.5}^2$ – ${2.5}^2$

${PT}^2$ = 42.25 – 6.25

${PT}^2$ = 36

PT = 6

Therefore the length of the tangent is 6 cm