Question

in a circle with centre P and radius 10cm, the angle between 2 radii segment PA and segment PB is 60°. find the length of chord AB​

Answer 1

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In a circle with centre P and radius 10cm, the angle between 2 radii segment PA and segment PB is 60°. find the length of chord AB.

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• Given PA and PB are tangents of a circle, PA= 10 cm and ∠APB=60∘

Let O be the center of the given circle and C be the point of intersection of OP and AB.

In ΔPAC and ΔPBC

PA=PB (Tangents from an external points are equally inclined to the segment joining center to that point)

PC=PC(Common)

Thus, ΔAPC is congruent to ΔPBC (By SAS congruency rule) _______ (1)

Also ∠APB=∠APC+∠BPC

∠APC= 1/2∠PAB[∵∠APC=∠BPC]

1/2 ×60∘

=30∘

But ∠ACP+∠BCP=180

[∠ACP=∠BCP=∠ACP= 1/2 ×180 ]

Now in right triangle ACP

sin30∘ = AC / AP

1/2 = AC/10

AC= 10/2

AC=5

∴AB+AC+BC=AC+AC(AC=BC)

∴ The length of the chord AB is 10 cm