Proportional segments in a circle
Answers are for parents and teachers.
1
Chords AB and CD meet at O: AO = 12, OB = 5, CO = 10. Find OD.
6
2
The tangent is PA = 12 and the outer part of the secant is PB = 9. Find PC.
16
3
In a circle of radius 7 the point P is 4 from the centre. A chord through P has the part AP = 3. Find PB.
11
4
AB is a diameter, CD ⟂ AB, AE = 4 and EB = 9. Find CD.
12
5
Why does PA² = PB·PC hold?
In triangles PAB and PCA the angle P is common and ∠PAB = ∠PCA, so they are similar.