Question

in figure ab is a chord of length 16 CM of a circle of radius 10 cm the tangents of A and B intersect at point P find the length of PA

Answer 1

*See attachment:

Given that AP and BP are tangents and O is the centre of the circle:

⇒ OP bisect AB in equal halves, AN and BN

Find the length AN:

Length of chord = 16 cm

Length of AN = BN = 16 ÷ 2 = 8 cm

Find ∠AOP:

sin(ø) = opp/hyp

sin(∠AOP) = AN/AO

sin(∠AOP) = 8/10

∠AOP = sin⁻¹ (8/10) = 53.13º

Find ∠AP0:

∠OAP = 90º (Tangent of the line and radius always form a 90º)

∠AP0 = 180 - ∠OAP - ∠AOP

∠AP0 = 180 - 90 - 53.13

∠APO = 36.87º

Find PA:

sin(ø) = opp/hyp

sin(∠APO) = AN/AP

sin(36.87º) = 8/AP

AP = 8/sin(36.87º)

AP = 13.33 cm

Answer: AP = 13.33 cm