Question

26. BOA is a diameter of a circle and the tangent at a point P meets BA produced at T. If &PBO 40"
then find PTA
​

Answer 1

Answer:

Step-by-step explanation:

Given, PT is a tangent

∠PBA=30  

0

 

Now,

∠BPA=90  

0

        (angle in semicircle)

∠OPT=90  

0

        (angle between the radius and tangent)

Also in ΔBPA

∠PAB=180  

0

−(∠30  

0

+∠BPA)

             =180  

0

−30  

0

−90  

0

 

             =60  

0

⟶(1)

Now look into the ΔOPA,

OP=OA (radius of circle)

⇒∠OAP=∠OPA=60  

0

        (∵∠OAP=∠BAP=60  

0

)

∴   ∠APT=∠OPT−∠OPA=90  

0

−60  

0

=30  

0

 

∴   ∠PAT=180  

0

−(60  

0

)=120  

0

          (supplementary angle)

In ΔPAT,

∠PAT+∠PTA+∠APT=180  

0

 

⇒120  

0

+∠PTA+30  

0

=180  

0

 

⇒∠PTA=30  

0

.

hope u get it!!