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Can someone please help I really need these points

Can someone please help I really need these points-example-1
User Jayanth Ramachandran
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2.6k points

1 Answer

29 votes
29 votes

Given:

Two chords intersect each other inside the circle.

To find:

The value of x.

Solution:

According to intersecting chords theorem, if two chords intersect each other inside the circle, then the product of two segments of one chord is equal to the product of two segments of second chord.

In the given circle,


AE* CE=BE* DE


(3x-11)* (5x-4)=(x+2)* (-x+17)


15x^2-12x-55x+44=-x^2+17x-2x+34


15x^2-67x+44+x^2-15x-34=0


16x^2-82x+10=0

Divide both sides by 2.


8x^2-41x+5=0

Splitting the middle term, we get


8x^2-40x-x+5=0


8x(x-5)-1(x-5)=0


(8x-1)(x-5)=0

Using zero product property, we get


(8x-1)=0 or
(x-5)=0


x=(1)/(8) or
x=5

For
x=(1)/(8), the side AE is negative. So,
x=(1)/(8) is not possible.

Therefore, the required solution is
x=5.

User Hamza Zafeer
by
3.1k points