Question

In the given figure, BA and DC are two chords of a circle intersecting each other
point P outside the circle. If PA-4 cm, PB-10 cm and CD-3 cm, find PC.
​

Answer 1

Length of PC = 5 cm

Step-by-step explanation:

The image of the question is attached below.

BA and DC are two chords of a circle intersecting each other  at point P outside the circle.

PA = 4 cm, PB = 10 cm, CD = 3 cm

Let PC = x and PD = 3 + x

Secant-secant theorem:

The product of one secant segment and its external segment is equal to the product of other secant segment and its external segment.

PA × PB = PC × PD

$4\times10=x(3+x)$

$40=3x+x^2$

$x^2+3x-40=0$

$(x-5)(x+8)=0$

x – 5 = 0, x + 8 = 0

x = 5, x = –8

Length cannot be measured in negative units. So ignore x = –8.

PC = 5 cm

To learn more...

1.AB and CD are two chords of a circle which intersect each other externally at P. If AB=4 cm, BP = 5 cm, PD = 3 cm, then the length of CD

https://brainly.in/question/3386839

2. BA and DC are two chords of a circle, which when extended meet at a point P outside the circle. If PA=4 cm, PB=10 cm and PC=5 cm then find the length of CD.

https://brainly.in/question/7750052