Question

AB is a chord of radius r. If p is any point on the circle such that angle APB is a right angle, then find the length AB
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Answer 1

Answer:

The line AC passes through O. So it is a diameter of the circle.

∴∠ABC is an angle inscribed in a semicircle.

∴∠ABC=90O. 

Now ∠ABC+∠ACB+∠BAC=180O   ...(sum of the { angles of a Δ=180O) 

⇒50O+90O+∠BAC=180O 

⇒∠BAC=40O 

Again, AT is a tangent to the circle at A.

∴∠CAT=90O

⇒∠BAT+∠CAB=90O 

⇒∠BAT+40o=90O 

⇒∠BAT=50O.