Question

- XY is a tangent to a circle with centre O touching the circle at Y. If OX = 61 cm
and the diameter of the circle is 22 cm, find XY.​

Answer 1

XY=60 cm

Step-by-step explanation:

Consider the provided information.

XY is a tangent to a circle with centre O touching the circle at Y.

Consider the figure shown below:

The diameter of the circle is 22 cm, that means the radius of the circle is 11 cm.

A line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency.

The triangle is a right angle triangle, where OY is the leg of the triangle and OX is the hypotenuse of the triangle.

By using the Pythagoras theorem:

$(OY)^2+(XY)^2=(OX)^2$

$(11)^2+(XY)^2=(61)^2$

$121+(XY)^2=3721$

$(XY)^2=3721-121$

$(XY)^2=3600$

$XY=60$

Hence, XY=60 cm

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Answer 2

Answer:

xy=60

Step-by-step explanation:

Consider the provided information.

XY is a tangent to a circle with centre O touching the circle at Y.

Consider the figure shown below:

The diameter of the circle is 22 cm, that means the radius of the circle is 11 cm.

A line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency.

The triangle is a right angle triangle, where OY is the leg of the triangle and OX is the hypotenuse of the triangle.

By using the Pythagoras theorem: