Choose the correct simplification of the expression (2x7y)2(y5)3.
1 answer:
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1. CD is tangent to the circle with center O, at point D.
2. Join D to O.
3. OD = OB = r, where r is the radius of the circle.
4. radius OD is perpendicular to the tangent CD.
5. Thus in the right triangle OCD:
, by the pythagorean theorem.
6.
Note: when applying pythagorean theorem, the difference of squares property
[
] is a useful practical tool in calculations.
38r=(35 -19)(35+19)
38r=16*54
r=
7. Finally, the diameter BA=2r=2*22.74=45.48
So the answer is 45.5
2. Join D to O.
3. OD = OB = r, where r is the radius of the circle.
4. radius OD is perpendicular to the tangent CD.
5. Thus in the right triangle OCD:
6.
Note: when applying pythagorean theorem, the difference of squares property
[
38r=(35 -19)(35+19)
38r=16*54
r=
7. Finally, the diameter BA=2r=2*22.74=45.48
So the answer is 45.5