PA and PB are the Tangents Drawn to a Circle with Centre O. If PA= 6 cm and APB=60 then Find the Length of the Chord AB | Bzziii.com

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PA and PB are the tangents drawn to a circle with centre O. If PA= 6 cm and APB=`60^0`, then find the length of the chord AB.






Given,

PA = PB (Tangent segments drawn to a circle from an external point are equal)

and  ∠APB = `60^0`

∴ In △APB, 
PA and PB are the Tangents Drawn to a Circle with Centre O. If PA= 6 cm and APB=60 then Find the Length of the Chord AB


∠PAB = ∠PBA 

In △APB, sum of three angles is 180°. 

Therefore, ∠PAB + ∠PBA + ∠APB = 180°

= ∠PAB + ∠PBA = 180° - ∠APB 

= ∠PAB + ∠PBA = 180° – 60° = 120°

∴ ∠PAB = ∠PBA = 60°  (∵ ∠PAB = ∠PBA) 

∵ △APB is an equilateral triangle. So, AB = 6 cm






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