The figure is a circle with center O.
Given PQ = 12 cm.
Find the length of segment PA.
(Figure may not be drawn to scale.)
a.
b.
24 cm
3 cm
c.
d.
12 cm
6 cm

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vijayalalitha vijayalalitha · Answer 1 · 2020-04-20T14:22:02+02:00

Given:

Given that the circle with center O.

The radius of the circle is OB.

The chord of the circle O is PQ and the length of PQ is 12 cm.

We need to determine the length of the segment PA.

Length of the segment PA:

We know that, "if a radius is perpendicular to the chord, then it bisects the chord and its arc".

Thus, we have;

[tex]PA=\frac{PQ}{2}[/tex]

Substituting the value PQ = 12, we get;

[tex]PA=\frac{12}{2}[/tex]

[tex]PA=6 \ cm[/tex]

Thus, the length of the segment PA is 6 cm.

Hence, Option d is the correct answer.

abidemiokin abidemiokin · Answer 2 · 2021-10-22T12:18:23+02:00

From the given figure with centre O and PQ as 12cm, the measure of the length PA is 6cm

From the given circle geometry, we can see that the line OB bisects the line PQ at A. This shows that;

PA = AQ ............................. 1

PA + AQ = PQ ..................... 2

Substitute equation 1 into 2

PA + PA = PQ

2PA = PQ

GIven that PQ = 12, substitute into the resulting expression:

PA = PQ/2

PA = 12/2

PA = 6cm

Hence from the given figure with centre O and PQ as 12cm, the measure of the length PA is 6cm

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