Forgetting tangent-radius is 90° H
"The Right Angle Oversight"
The Mistake in Action
PT is a tangent to the circle at T. O is the centre. Angle OPT = 35°. Find angle POT.
Wrong: Cannot be found without more information.
Why It Happens
Students don't automatically recognise that tangent-radius creates a right angle, so they think they don't have enough information.
The Fix
Key fact: The angle between a tangent and radius is always 90° at the point of contact.
In triangle OPT:
- Angle OTP = 90° (tangent ⊥ radius)
- Angle OPT = 35° (given)
- Angle POT = 180° - 90° - 35° = 55°
Always look for tangent lines — they create right angles with the radius!
Spot the Mistake
Can you identify where this student went wrong?
PT is tangent at T, angle OPT = 35°
Cannot be found
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: