In the adjoining figure, if the angle between two radii of a circle is 130°, then find the angle between the tangent at the ends of the radii.
(Class 10 Maths Sample Question Paper)
(Class 10 Maths Sample Question Paper)
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SOLUTION:[FIGURE IS IN THE ATTACHMENT]
Given:∠AOB = 130 ° ………….(1)
∠PAO = ∠PBO = 90 °………….(2)
[ Radius is perpendicular to the tangent at the point of contact .]
On applying angle sum property in quadrilateral OAPB
∠PAO +∠AOB+∠OBP+ ∠APB = 360 °
90° + 130 ° + 90 ° + ∠APB = 360 °
[ From equation 1 and 2]
310° + ∠APB = 360 °
∠APB = 360 ° - 310°
∠APB = 50°
Hence, the angle between the tangent at the ends of the radii is 50°.
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