Question 1191626: The tangent PT to a circle touches the circle at P. If the radius of the circle is 2.8cm and OT is 5.5cm, calculate the length of the tangent
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! OP is equal to 2.8 cm.
OT is equal to 5.5.
right triangle OPT is formed with OT as the hypotenuse and OP as one of the legs.
PT is the other leg, which is also the tangent line to the circle.
OPT is the right angle.
let OP = x and PT = y and OT = z.
by pythagorus, z^2 = x^2 + y^2
replace x with 2.8 because that's the length of OP, and replace z with 5.5 because that's the length of OT, and you get 2.8^2 + y^2 = 5.5^2.
solve for y^2 to get y^2 = 5.5^2 - 2.8^2 = 22.41.
solve for y to get y = sqrt(22.41) = 4.733920151.
that's the length of PT which is the tangent.
that should be your answer.
you can say it's sqrt(22.41) or you can say it's 4.733920151.
you can round 4.733920151 as required, if that's the way they want to see the answer.
the answer depends on the fact that the tangent to a circle is perpendicular to the radius of the circle at the point of tangency.
here's a reference on tangent to a circle.
https://www.cuemath.com/geometry/tangent/
let me know if you have any questions or concerns.
theo
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