Concept of circle and triangle

Question

The equation of side opposite to vertex (a,0)?

(a) !!2x-a = 0!!

(b) !!x+a = 0!!

(c) !!2x+a = 0!!

(d) !!3x-2a = 0!!

Solution

Suppose !!P(a,0), A(x_1,y_1)!! and !!B(x_1,y_2)!!

Since length of the sides are equal,

!!PA = PB!!

!!=> (x_1-a)^2+y_1^2 = (x_1-a)^2+y_2^2!!

!!=> y_1= +- y_2= y!!

Equation of !!AB!!,

!!x= -x_1 ...(1)!!

We can find !!OC, x_1= a cos60^0= a/2!!

!!=> x_1= a/2!!

Putting the value of !!x_1!! in equation (1), we get

!!x= -a/2 => 2x+a=0!!

Therfore, correct option is (c).

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