Q1. What is the angle between a tangent and the radius at the point of contact?
✔ The theorem states the tangent is perpendicular to the radius, meaning the angle is exactly ninety degrees.
Q2. If radius is 3 cm and tangent is 4 cm, what is the distance from center to external point?
✔ Using Pythagoras theorem, the square root of nine plus sixteen equals five centimeters.
Q3. How many tangents can be drawn from a single point on the circle?
✔ From any point on the circumference, exactly one tangent line can be drawn perpendicular to the radius.
Show transcript
[Slide 1] Visualizing the Tangent
Think of a wheel touching the ground. The line from center to touch point is perpendicular. This prevents the wheel from sliding sideways.
[Slide 2] The Tangent Radius Theorem
This theorem states the tangent line is perpendicular to the radius. It happens exactly at the point of contact. Always remember this creates a right angle.
[Slide 3] Solving a Real Problem
Let us solve a problem with real numbers. The radius is three centimeters and tangent is four. We must find the distance from center to point P.
[Slide 4] Applying Pythagoras Theorem
Since we have a right angled triangle, use Pythagoras theorem. Add the squares of radius and tangent lengths. The square root of twenty-five is five.
[Slide 5] Avoiding Common Errors
Students often forget to mark the right angle. Sometimes they mistake the tangent for the hypotenuse. Remember the line from center is always hypotenuse.
[Slide 6] Key Takeaways Summary
Remember the tangent touches at only one point. The radius is always perpendicular to this line. This helps solve many geometry problems easily.