Question

Chord AC intersects chord BD at point P in circle Z.

AP=4 cm
BP=5 cm
PC=8 cm



What is PD?

Enter your answer as a decimal in the box

Answer 1

Using the chord intersection theorem, AP · PC = BP · PD
Thus, 4 · 8 = 5 · PD
32 = 5PD
PD = 6.4 cm

Answer 2

Answer: 6.4 cm

Explanation:

By the internal intersection of chords theorem,

When two chords intersect each other inside a circle, the products of their segments are equal.

In the given diagram, the chords AC and BD are intersecting internally at point P,

Thus, We can write,

`BP* PD = AP* PC`

`\implies 5* PD = 4* 8`

`\implies 5PD=32`

`\implies PD = 6.4`

Hence, the measurement of segment PD = 6.4 cm.