Question

the radius of the circle is 5cm and 13cm . find the area of sector

Answer 1

QUESTION

In figure O is the centre of a circle of radius 5 cm, T is a point such that OT=13 cm ad OT intersects the circle at E . If AB is the tangent to the circle at E, find the length of AB.
ANSWER
Given, OT = 13, OP = OQ = 5
From the figure,
By Pythagoras Theorem,
      (OT)2 = (OP)2 - (PT)2
=> (13)2 = 52 - (PT)2
=> 169 = 25 - (PT)2
=> (PT)2 = 169 - 25
=> (PT)2 = 144
=> PT = √144
=> PT = 12
Thus, PT = QT = 12
Now, let AB = x and BT =  y
from the figure,
ET = OT - OE = 13 - 5 = 8
Since AB is a tangent to he circle and OE is the radius of the circle
=> OE ⊥ AB
Hence, TE bisects AB
=> AE = EB/2 = x/2
Again, the length of the tangents from a point to the circle are equal.
So, EB = QB = x/2
Now, QT = QB + BT
=> 12 = x/2 + y
=> y = 12 - x/2 ..................1
From triangle BET,
By Pythagorus Theorem,
      (TE)2 + (BE)2 = (BT)2
=> 82 + (x/2)2 = y2
=> 64 + x2 /4 = (12 - x/2)2
=> 64 + x2 /4 = 144 + x2 /4 - 24x/2
=> 64 = 144 - 24x/2
=>12x = 144 - 64
=> 12x = 80
 => x = 80/12
=> x = 20/3
So, the length fo AB is 20/3 cm
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ANSWER IS FROM GOOGLE....