Question

The angle between the two radius of a circle is 130° then the angle between the tangents drawn at the end of the radius is

Options
A. 65°
B. 40°
C. 70°
D. 50°​

Answer 1

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

$\huge\mathfrak{Explanation}$

➠ 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°.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━