Question

If pa and pb are two tangents drawn to a circle with centre o , from an external point p such that pa=5cm and apb = 60 , then find the length of the chord ab.

Answer 1

Answer:

Length of chord AB is 5 cm.

Step-by-step explanation:

If PA and PB are two tangents drawn to a circle with center O

Such that PA=5 cm and ∠APB=60°

Join PO, PO is bisect the ∠APB=60°

Therefore, ∠APO=30°

AB is chord of a circle. Line OP is perpendicular to AB at M

In ΔAPM, ∠AMP=90°

$\sin (\angle APM)=\frac{AM}{AP}$

$\sin 30^{\circ}=\frac{AM}{5}$

$\frac{1}{2}=\frac{AM}{5}$

$AM=\frac{5}{2}$

AB is 2 times of AM

AB=2 x AM = 5

Thus, Length of chord AB is 5 cm.

Answer 2

Step-by-step explanation:

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