Question

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)

Answer 1

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°.

HOPE THIS WILL HELP YOU....

Answer 2

hello friend,
the angle formed between the tangents will be 50°.
hope it helps you :-)