Question

if a chord AB subtends an angle 50degree at the centre of a circle, then what is the angle between the tangents A and B​

Answer 1

Answer:

130°

Step-by-step explanation:

Let us assume that A and B are the two points on a Circle having center at O.

Now join A, O and B, O.

So, OA and OB become two radius of the Circle.

Again, AB becomes one of the chord of the Circle.

Given that ∠AOB =50°.

Now draw two tangents to the circle at points A & B and assume that two tangents meet at point P.

We have to find out ∠APB.

It is clear that AOBP is a quadrilateral and

∠O+∠A+∠P+∠B= 360° ...... (1)

Now, ∠OAP = 90° [ as AO is the radius of the circle and AP is a tangent to it, so OA⊥AP]

Similarly, ∠OBP = 90°

So, from (1), ∠O+∠P= 360°-90°-90°= 180° .....(2)

Now, given that ∠O=50°

So, from (2), ∠APB = 180°-50°= 130°