(i) In the given figure, 3 x CP = PD = 9 cm and AP = 4.5 cm. Find BP. (ii) In the given figure, 5 x PA = 3 x AB = 30 cm and PC = 4cm. Find CD. - Noon Academy

(i) In the given figure, 3 x CP = PD = 9 cm and AP = 4.5 cm. Find BP. (ii) In the given figure, 5 x PA = 3 x AB = 30 cm and PC = 4cm. Find CD.

Class 10 | Exercise 18B | ICSE | Maths | Selina | Tangents and Intersecting Chords

(i) In the given figure, 3 x CP = PD = 9 cm and AP = 4.5 cm. Find BP. (ii) In the given figure, 5 x PA = 3 x AB = 30 cm and PC = 4cm. Find CD.

(i)

Selina Solutions Concise Class 10 Maths Chapter 18 ex. 18(B) - 1

(ii)

Selina Solutions Concise Class 10 Maths Chapter 18 ex. 18(B) - 2

Solution:

(i) As the two chords

$AB\text{ }and\text{ }CD$

intersect each other at

$P$

We have

$AP\text{ }x\text{ }PB\text{ }=\text{ }CP\text{ }x\text{ }PD$

$4.5\text{ }x\text{ }PB\text{ }=\text{ }3\text{ }x\text{ }9$

$\left[ 3CP\text{ }=\text{ }9\text{ }cm\text{ }so,\text{ }CP\text{ }=\text{ }3\text{ }cm \right]$

$PB\text{ }=\text{ }\left( 3\text{ }x\text{ }9 \right)/\text{ }4.5\text{ }=\text{ }6\text{ }cm$

(ii) As the two chords

$AB\text{ }and\text{ }CD$

intersect each other at

$P$

,

we have

$AP\text{ }x\text{ }PB\text{ }=\text{ }CP\text{ }x\text{ }PD$

But,

$5\text{ }x\text{ }PA\text{ }=\text{ }3\text{ }x\text{ }AB\text{ }=\text{ }30\text{ }cm$

So,

$PA\text{ }=\text{ }30/5\text{ }=\text{ }6\text{ }cm$

And

$AB\text{ }=\text{ }30/3\text{ }=\text{ }10\text{ }cm$

And,

$BP\text{ }=\text{ }PA\text{ }+\text{ }AB\text{ }=\text{ }6\text{ }+\text{ }10\text{ }=\text{ }16\text{ }cm$

Now, as

$AP\text{ }x\text{ }PB\text{ }=\text{ }CP\text{ }x\text{ }PD$

$6\text{ }x\text{ }16\text{ }=\text{ }4\text{ }x\text{ }PD$

$PD\text{ }=\text{ }\left( 6\text{ }x\text{ }16 \right)/\text{ }4\text{ }=\text{ }24\text{ }cm$

So,

$CD\text{ }=\text{ }PD\text{ }-\text{ }PC$

$=\text{ }24\text{ }-\text{ }4\text{ }=\text{ }20\text{ }cm$

i

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