Question

In Figure-3. PT is tangent to a circle centred at O. Find the value of
angle OTP if angle POT = 75°.​

Answer 1

If we extend OT
Angle in semi Circle is 90
Then in triangle OTP,

75+90+x=180
Since OTP = 15

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Answer 2

In Figure-3. PT is tangent to a circle centred at O.

Consider the figure while going through the following steps.

Given,

∠ POT = 75°

OP = radius of the circle

PT = tangent to the circle.

We know that, the radius is perpendicular to the tangent.

⇒ OP ⊥ PT

∴ ∠ OPT = 90°

Now consider, in Δ OPT,

∠ OPT + ∠ OTP + ∠ POT = 180°  

(∵ sum of interior angles of a triangle equals 180°)

⇒ 90° + ∠ OTP + 75° = 180°

165° + ∠ OTP = 180°

∠ OTP = 180° - 165°

∴ ∠ OTP = 15°