Question

7. AABC is a triangle such that 2C = 90. Suppose AC 12 cm, AB - 13 cm and the perpendicular
distance from C to AB is x cm. Find the value of x.​

Answer 1

Answer:

Step-by-step explanation:

In △ABC,

⇒  ∠B=90  

o

             [ Given ]

⇒  AB=12cm and AC=13cm           [ Given ]

Here, O is center of a circle and x is a radius.

⇒  (AC)  

2

=(AB)  

2

+(BC)  

2

               [ By Pythagoras theorem ]

⇒  (13)  

2

=(12)  

2

+(BC)  

2

 

⇒  169=144+(BC)  

2

 

⇒  (BC)  

2

=25

∴  BC=5cm

Now, AB,BC and CA are tangents to the circle at P,N and M respectively.

∴  OP=ON=OM=x          [ Radius of a circle ]

⇒  Area of △ABC=  

2

1

​

×BC×AB

                                 

                                 =  

2

1

​

×5×12

                                 =30cm  

2

 

Area of △ABC= Area of △OAB+ Area of △OBC+ Area of △OCA

⇒  30=  

2

1

​

x×AB+  

2

1

​

x×BC+  

2

1

​

x×CA

⇒  30=  

2

1

​

x(AB+BC+CA)

⇒  x=  

AB+BC+CA

2×30

​

 

⇒  x=  

12+5+13

60

​

 

⇒  x=  

30

60

​

 

∴   x=2cm

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