Question

if chord ab subtends an angle 50degree at the centre of the circle then the angle between the tangents at a and b is​

Answer 1

Answer:

130°

Explanation:

As we know tangents creates an angle of 90° with the radius on a single point, here OA⊥AC & OB⊥BC

Therefore, making ∠CAO = ∠CBO = 90°

We know in a quadrilateral the sum of the four angles is 360°.

Check the image attached, thus

∠AOB + ∠OBC + ∠BCA + ∠CAO = 360°

As per the question, ∠AOB = 50°

We've to determine the angle(question marked in the image) ∠BCA

or, ∠BCA = 360° - (∠AOB + ∠OBC + ∠CAO)

or, ∠BCA = 360° - (50° + 90° + 90°)

or, ∠BCA = 130°