Question

In the given figure, O is the center of each one of two concentric circles of radii 4 cm and 6 cm respectively. PA and PB are tangents to outer and inner circle respectively. If PA = 10 cm, find the length of PB(up to two places of decimal).

Answer 1

Join AO, BO, PO

Given that AO = 6 cm, PA = 10 cm, OB = 4 cm

Applying Pythagoras theorem to $△$OAP

${PO}^2$ = ${AO}^2$ + ${PA}^2$

${PO}^2$ = 36 + 100

${PO}^2$ = 136

Applying Pythagoras theorem to ΔOBP

${PB}^2$ = ${PO}^2$ - ${BO}^2$

${PB}^2$ = 136 - $4^2$

${PB}^2$ = 120

PB= 10.95