Question

Tangent of a circle with center O, touches XY. Circle at point Y. If OX=61cm and diameter of a circle is 22cm , then find XY.​

Answer 1

Answer:

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(OY)

2

+(XY)

2

=(OX)

2

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

2

+(XY)

2

=(61)

2

121+(XY)^2=3721121+(XY)

2

=3721

(XY)^2=3721-121(XY)

2

=3721−121

(XY)^2=3600(XY)

2

=3600

XY=60XY=60

Hence, XY=60 cm

Step-by-step explanation:

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