Idon't understand how to prove that this is an isosceles triangle.

Check the picture below.

so, two tangents to the same circle, whenever they meet outside the circle, they'll be congruent, namely, AB = AX and CB = CY and DX = DY.

well, we know AB = BC, and we know that AB = AX and CB = CY, therefore

AB = BC = AX = CY = 10.

an isosceles needs twin sides, well, we know DX = DY, and we know that AX = 10 then the triangle's side AD = AX + DX = 10 + DX.

the triangle's side of CD = CY + DY = 10 + DY.

but but but, we know DX and DY are tangents to a common circle meeting outside, so they're equal, so whatever length DX and DY are, is the same, so

10 + DY = 10 + DX

meaning the triangle's sides AX = CD, and for an isosceles, is all you need, twin sides.

step-by-step explanation:

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