Question

In the figure angle APB=60degree's
and OP =10cm then PA=?

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Answer 1

Answer:

$AP = 5cm$

Step-by-step explanation:

In the fig.

Consider ΔAOP &ΔBOP

OA = OB (∵radii of the circle)

OP = OP ( ∵common)

∠OAP = ∠OBP ( ∵ the angle subtended by a tangent is⊥ to the radius  

                                                            `through  point of contact )

⇒Δ OAP ≅ Δ OBP ( SAS congruence rule)

⇒ AP = BP ( C.P.C.T.)           [i]

⇒ ∠OPA = ∠OPB (C.P.C.T.) [ii]

Now

∠OPA = $\frac{<APB}{2}$      [ From eq ii]

∴∠OPA = ∠OPB =  30°

Now

In ΔAOP

OP = 10 cm (given)

cos60° = $\frac{1}{2}$

$\frac{AP}{OP}$ =  $\frac{1}{2}$

$\frac{AP}{10}$ = $\frac{1}{2}$

⇒$AP = 5cm$ Ans.