Does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?​
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Step-by-step explanation:

The solution and answer are well written in the Pic above.

Given equation of the Circle is ,

And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,

Here we can say that ,

• Radius = 5 units

• Centre = (0,0)

Finding distance between the two points :-

Here we can see that the distance of point from centre is less than the radius.

Hence the point lies within the circle .

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4