Question

AT is a tangent to a circle at A with centre 0 from an external point T, such that OT = 8cm and
OTA = 30°. The length of AT (in cm) is
[ ]
a) 2
b) 32
c) 43
d) 4


please check and solve it fast

the answer was given as option 'd'

please fastttttttttt
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Answer 1

Answer:

2

Step-by-step explanation:

See the image attached:

Draw a perpendicular on AT

From the property we know that perpendicular drawn on the tangent divided the tangent in 2 equal parts. Let it be OC

Now,

     cos30 = CT/OT

     root3/2 = CT/4

     CT = 4root3

Now AT = CT + CA

        AT = 8root2

       AT = 2 (approx)

Option A