Question

-) In the figure, BP = 16 cm, CP = 18 cm,
DC = 14 cm. Calculate
(i) the length of chord AB
(ii) the length of tangent PT​

Answer 1

-) In the figure, BP = 16 cm, CP = 18 cm,  DC = 14 cm.

(i) the length of chord AB

we know that, the lengths of secants drawn from an external point to the circle are equal. Therefore, we have,

PA = PD

PB + BA = PC + CD

16 + AB = 18 + 14

16 + AB = 32

AB = 32 - 16

∴ AB = 16 cm

(ii) the length of tangent PT​

PT² = DP × PC

PA = PB + BA = 16 + 16 = 32 cm

PA = DP = 32 cm

PC = 18 cm

PT² = 32 × 18

PT² = 576

∴ PT = 24 cm