Question

In a circle with center seg OP chord AB, AB= 48 cm, OP = 7 cm then find radius of the circle. ​

Answer 1

Step-by-step explanation:

Solution:

Given that:

BP=4PA,OP=5cm and OA=OB=7cm

To find:

6

​

×AB=?

Solution:

Let PA=x,BP=4x

AB=PA+BP=x+4x=5x

BM=AM=  

2

AB

​

=  

2

5x

​

 

and MP=  

2

5x

​

−x=  

2

3x

​

 

In △OMB

OB  

2

=OM  

2

+BM  

2

    (By pythagorus theorem)

or, OM  

2

=7  

2

−(  

2

5x

​

)  

2

=49−  

4

25x  

2

 

​

 

In △OMP

OP  

2

=MP  

2

+OM  

2

    (By pythagorus theorem)

or, 5  

2

=(  

2

3x

​

)  

2

+49−  

4

25x  

2

 

​

 

or, 25=  

4

9x  

2

 

​

+49−  

4

25x  

2

 

​

 

or, 4x  

2

=24

or, x  

2

=6

or, x=  

6

​

 

AB=5x=5  

6

​

 

or,  

6

​

×AB=  

6

​

×5  

6

​

=30cm