Question

prove that the tangents at the extremities of a chord

Answer 1

GIVEN ;-

⇒ O is the centre of the circle.

⇒ PQ is the chord of the circle.

⇒ AP and AQ are the tangents at points P and Q.

⇒ AP and AQ are the tangents which meet at pont - A.


CONSTRUCTION ;-

⇒ Join the  points - O, and  P.


TO PROVE ;-

⇒ ∠APR = ∠AQR


PROOF ;-

⇒ Now in triangle APR and AQR,
 
                       ⇒ AR = AR { common side }
    
                        ⇒ AP = AQ [ They are the Tangents which are  drawn from an                                             internal point to a circle  are equal

                       ⇒ ∠ PAR = ∠ QAR 

So by SAS congruence rule we say that ,
 
                      ⇒ ΔAPR ≅ ΔAQR

And through C. P. C.T { corresponding parts of congruent triangles }
We say that ,

                        ⇒ ∠APR = ∠AQR

Hence proved .

Answer 2

Answer:

Step-by-step explanation: