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AB is the diameter of the circle and ∠PAB=40∘

what is the value of ∠PCA?


376998

  • a)
    50∘

  • b)
    55°

  • c)
    70° 

  • d)
    45°

Correct answer is option 'A'. Can you explain this answer?
Verified Answer
AB is the diameter of the circle and∠PAB=40what is the value of&an...


  • In △PAB


    ⇒  ∠PAB=40o         [ Given ]


    ⇒  ∠BPA=90o      [ angle inscribed in a semi-circle ]


    ⇒  ∠PAB+∠PBA+∠BPA=180o


    ∴   40o+∠PBA+90o=180o


    ∴   ∠PBA=180o−130o


    ∴   ∠PBA=50o


    ⇒  ∠PBA=∠PCA=50o     [ angles inscribed in a same arc PA ] 


    ∴   ∠PCA=50o


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Most Upvoted Answer
AB is the diameter of the circle and∠PAB=40what is the value of&an...
This is based on the Chord Theorem : 
The angle subtended by an arc at the center of a circle is double that of the angle that the arc subtends at any other given point on the circle.
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AB is the diameter of the circle and∠PAB=40what is the value of∠PCA?a)50b)55°c)70°d)45°Correct answer is option 'A'. Can you explain this answer?
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