Question

if the angle between two radii of a circle is 130 degree then find the angle between tangents at the end of radii

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Answer 1

Angle subtended between 2 tangents is supplementary with the angle subtended between the two radii of the same circle

Answer 2

Answer:

The angle between the tangent at the ends of the radii is 50°

Step-by-step explanation:

Given the angle between two radii of a circle is 130 degree.

we have to find the angle between tangents at the end of radii

∠AOB = 130 ° ………….(1)

By theorem, radius is perpendicular to the tangent at the point of contact

∴ ∠PAO = ∠PBO = 90 °………….(2)

By angle sum property in quadrilateral OAPB

∠PAO +∠AOB+∠OBP+∠APB = 360°

90° + 130° + 90° + ∠APB = 360°

310° + ∠APB = 360 °

∠APB = 360 ° - 310°

∠APB = 50°

Hence, the angle between the tangent at the ends of the radii is 50°.