Two chords AB and CD intersect at a point P inside a circle. If AP = 4\text{ cm}, PB = 9\t… — JAMB UTME

Two chords $AB$ and $CD$ intersect at a point $P$ inside a circle. If $AP = 4\text{ cm}$ , $PB = 9\text{ cm}$ , and $CP = 3\text{ cm}$ , what is the length of segment $PD$ in centimeters?

Answer: 12 cm

Answer

The length of segment

PD

12\text{ cm}

According to the Intersecting Chords Theorem, for two chords intersecting inside a circle at point

P

, the relation

AP \times PB = CP \times PD

holds true. Substituting

AP = 4

PB = 9

, and

CP = 3

gives

4 \times 9 = 3 \times PD

, so

36 = 3 \times PD

, which yields

PD = 12\text{ cm}

Step-by-Step Solution

Apply the Intersecting Chords Theorem

AP \times PB = CP \times PD

When two chords intersect inside a circle, the product of the segments of one chord equals the product of the segments of the other.

Substitute the known values

4 \times 9 = 3 \times PD

, which gives

36 = 3 \times PD

Insert the values

AP = 4\text{ cm}

PB = 9\text{ cm}

, and

CP = 3\text{ cm}

Solve for

PD

PD = 12\text{ cm}

Divide both sides of the equation by 3.

Key Concept

Intersecting Chords Theorem

Question

Answer

Step-by-Step Solution

Key Concept

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