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Point 0 is the center of the circle, What is the value of X

Point 0 Is The Center Of The Circle What Is The Value Of X class=

Sagot :

Answer: x = 22

Explanation:

From the information given. O is the center of the circle. The distance from the center of the circle to the circumference is the radius. This means that

OQ = radius

O to the vertex where angle 56 is formed is also a radius

This means that two sides the triangle formed insides the circle are equal. This also means that this triangle is an isosceles triangle. The base angles of an isosceles triangle are equal. This means that

angle 56 = angle Q because they are the base angles of the isosceles triangle

Recall, the sum of the angles in a triangle is 180 degrees. This means that

angle O + 56 + 56 = 180

angle O + 112 = 180

angle O = 180 - 112

angle O = 68

Recall, the angle formed by a tangent with the radius of the circle is 90 degrees. This means that angle Q = 90 degrees

Considering triangle POQ,

angle P + angle O + angle Q = 180

x + 68 + 90 = 180

x + 158 = 180

x = 180 - 158

x = 22

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