ayanaji1122
ayanaji1122 ayanaji1122
  • 26-02-2021
  • Mathematics
contestada

prove that AB is tangent to circle

prove that AB is tangent to circle class=

Respuesta :

Hrishii
Hrishii Hrishii
  • 26-02-2021

Answer:

See Explanation

Step-by-step explanation:

[tex] AB^2 +OB^2 = 4^2 +3^2 = 16 + 9 =25[/tex]

.....(1)

[tex] OA^2 = 5^2 = 25[/tex]

..... (2)

From equations (1) & (2)

[tex] AB^2 +OB^2 = OA^2[/tex]

Therefore, by converse of Pythagoras theorem, triangle ABO is right angled triangle right angle at B.

Therefore,

Radius OB is perpendicular to AB.

Hence, AB is tangent to the circle with center O at point B.

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