Question

If PA and PB are tangents from an external point P to a circle, such that AP = 12 cm and LAPB -
60°. Find the length of chord AB​

Answer 1

Step-by-step explanation:

∠APO = ∠OPB = 1/2 × 60° = 30°

the chord AB will be bisected perpendicularly ∴

AB = 2AM

In ∆AMP,

AM /AP =sin 30°

AM = AP sin 30°

AP/2 = 12/2 = 6cm [As AB = 2AM]

So, AP = 2 AM = 12cm

And, AB = 2 AM =12cm

Alternate method: In ∆AMP, ∠AMP = 90°,

∠APM = 30°

∠AMP + ∠APM + ∠MAP = 180°

90° + 30° + ∠MAP = 180°

∠MAP = 60°

In ∆PAB, ∠MAP = ∠BAP = 60°,

∠APB = 60°

We also get, ∠PBA = 60°

∴ ∆PAB is equilateral triangle

AB=AP=12