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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

Chord AC intersects chord BD at point P in circle Z AP4 cm BP5 cm PC8 cm What is PD Enter your answer as a decimal in the box class=

Respuesta :

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

Answer: 6.4 cm

Step-by-step 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,

[tex]BP\times PD = AP\times PC[/tex]

[tex]\implies 5\times PD = 4\times 8[/tex]

[tex]\implies 5PD=32[/tex]

[tex]\implies PD = 6.4[/tex]

Hence, the measurement of segment PD = 6.4 cm.

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