Question

iii)
As shown in the adjoining figure line AP is
a tangent and line CP is a secant to the
circle.
If AP= 15 and BP
10 then find BC.​

Answer 1

Given:

• AP = 15cm
• BP = 10cm

Find:

• BC = ?

Solution:

Let, BC = 'x' cm

Since, PC is secant and AP is tangent

So,

↬ PA² = PC×PB

where,

• PA = 15cm
• PB = 10cm
• PB = 10 + x cm

☍ Substituting these values ☍

➣ PA² = PC×PB

➣ 15² = (10+x) × 10

➣ 225 = 100 + 10x

➣ 225 - 100 = 10x

➣ 125 = 10x

➣ 125/10 = x

➣ 12.5cm = x

➣ x = 12.5cm

Hence, value of BC = x = 12.5cm

Answer 2

Question :

★ As shown in the adjoining figure line AP is a tangent and line CP is a secant to the circle. If AP = 15 and BP = 10 then find BC. [ Figure or attachment ]

Given that :

★ Line AP or PA is a tangent

★ Line CP or PC is a secant to the circle.

★ AP = 15

★ BP = 10

To find :

★ Measure of BC.

Solution :

★ Measure of BC = 12.5 cm

Full solution :

As we know that here,

★ Line AP is a tangent and line CP is a secant to the circle.

★ AP = 15

★ BP = 10

★ And we have to find the measure of BC

★ Let a is the measure of BC.

Henceforth, 10 + a is measure of PB

So,

➝ PA² = PC × PB (Relationship to tagnet-secant therom).

➝ PC × PB = PA² (Relationship to tagnet-secant therom).

Note - We use or write PA² = PC × PB here because of a very easy reason and the reason is that according to the question, (work according to the question always) it is said that there is a secant and a tangent here (circle according to the figure) So according to this data it's cleared that we have to use

Knowledge (This topic) -

⚕️ What is secant and a tangent ?

Secant - The ratio of the hypotenuse to the shorer side to an acute angle. But it happen in just right angled triangle ∆.

Secant is defined as this also -

A straight line that cuts a curve figure into two and more parts.

Tangent - It's that line which touch a curve or curved surface but not the point.

$\rule{150}{1}$

According to the question let's move on,

Here,

☃ PA is 15

☃ PC is 10 + a

☃ PB is 10

➝ 15² = (10 + a) × 10

➝ 225 = (10 + a) × 10

➝ 225 = 10a + 100

➝ 225 - 100 = 10a

➝ 125 = 10a

➝ 125 / 10 = a

➝ 12.5 = a

➝ a = 12.5 cm