Explore the parts of a circle and their relationships — chords, tangents, and the special properties they follow.
A chord is a line segment joining two points on a circle. A key property: the perpendicular from the center of a circle to a chord always bisects that chord (cuts it exactly in half).
A chord is 16cm long, and the perpendicular from the center bisects it. How long is each half?
8cm, since the perpendicular bisects the chord exactly
If a chord's midpoint is found, what can you say about the line from the center to that midpoint?
It's perpendicular to the chord
A tangent is a line that touches a circle at exactly one point. A key property: a tangent line is always perpendicular to the radius drawn to the point of contact.
A tangent touches a circle at point P. What angle does it make with the radius drawn to P?
90°, since a tangent is always perpendicular to the radius at the point of contact
From an external point, two tangents are drawn to a circle. What's true about their lengths?
They are equal in length
1. A chord is 24cm long, and the perpendicular from the center bisects it. How long is each half?
2. A radius is drawn to the point where a tangent touches a circle. What angle is formed between them?
3. From an external point, two tangents are drawn to a circle, and one is 7cm long. How long is the other?
4. If a chord is 10cm from the center's perpendicular distance and the radius is unknown, what does the perpendicular from the center do to the chord?
5. A circle has a chord of length 30cm, bisected by a perpendicular from the center. If the radius is 17cm, find the distance from the center to the chord (Hint: use the Pythagoras theorem with half the chord).