Question

In the diagram, TA is a tangent to the circle at A. If 520, find

Answer 1

Answer:

find what first complete your question mate

Answer 2

Answer:

Step-by-step explanation:

In order to prove that  △ADT  is isosceles  i.e., TA = TD, it is sufficient to show that  ∠TAD = ∠TDA.

Since ∠TAB and ∠BCA are angles in the alternate segments of chord AB.

∴    ∠TAB = ∠BCA       …….(i)

It is given that AD is the bisector of ∠BAC.

∴         ∠BAD = ∠CAD           ……..(ii)

Now,   ∠TAD = ∠TAB + ∠BAD

⇒    ∠TAD = ∠BCA + ∠CAD      [Using (i) and (ii)]

⇒ ∠TAD  =  ∠DCA + ∠CAD       [∵  ∠BCA = ∠DCA]

⇒   ∠TAD  = 180˚ - ∠CDA    [In △CAD,  ∠CAD + ∠DCA + ∠CDA = 180˚]

∴     ∠CAD + ∠BCA = 180˚ - ∠CDA]

⇒ ∠TAD = ∠TDA      [∵   ∠CDA +  ∠TDA = 180˚]

⇒    TD = TA

Hence, △ADT  is isosceles .  

Hence proved.