Question

Chord AC intersects chord BD at point P in circle Z. AP=4 cm BP=5 cm PC=8 cm What is PD?

Answer 1

`32/5=6.4 cm`

Explanation:

Intersecting Chord Theorem : when two chords intersect each other inside a circle, the products of their segments are equal.

This theorem states that `AxxB` is always equal to `CxxD` no matter where the chords are.

Back to our question,
Given `AP=4, PC=8, and BP=5`,
and by Intersecting Chord Theorem, we get,
`APxxPC=BPxxPD`

`=> PD=(APxxPC)/(BP)=(4xx8)/5=32/5=6.4 cm`