PEAZIT Aha card
Go straight to resources ↓The radius meets a tangent at a right angle
A tangent touches the circle at one point T. Radius OT is perpendicular to the tangent, making triangle OPT right-angled at T.
| Relation | Meaning |
|---|---|
| OT ⟂ PT | The right angle is at the contact point, not the center. |
| PT² = OP² − OT² | OP is the hypotenuse: subtract OT² from its square. |
| PT = √(13² − 5²) = 12 | The square root of 144 gives tangent segment 12 cm. |
One worked example
- OT ⟂ PTThe right angle is at the contact point, not the center.
- PT² = OP² − OT²OP is the hypotenuse: subtract OT² from its square.
- PT = √(13² − 5²) = 12The square root of 144 gives tangent segment 12 cm.
Watch out: P must lie outside the circle. PT measures the segment to the contact point, not the infinite tangent line.
Goal, prerequisites and card origin
What you will learn: Use the right angle between radius and tangent.
What you need first: The Pythagorean theorem and square roots.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
A tangent touches the circle at one point T. Radius OT is perpendicular to the tangent, making triangle OPT right-angled at T.