Question

14. In the following figure, M is the midpoint of

(FA) and (MA) and (MB) are the tangents issued
from M to the circle(C).
F
M
B
(C)
question: Show that ABF is a right triangle.​

Answer 1

To show that ABF is a right triangle, we need to prove that angle BAF is 90 degrees. Given that FM is the midpoint of FA and MA, and MB are tangents to the circle, we can use properties of tangent lines.

Step-by-step explanation:

To show that ABF is a right triangle, we need to prove that angle BAF is 90 degrees. Given that FM is the midpoint of FA and MA, and MB are tangents to the circle, we can use properties of tangent lines. One property states that the tangent line is perpendicular to the radius at the point of contact. Since MB is tangent to the circle, angle MBF is 90 degrees. And since M is the midpoint of FA, angle MAF is also 90 degrees. Therefore, ABF is a right triangle.

Answer 2

angle OAM and OBM are right angles because tangents form right angles with radii.

AO=BO and MA=MB

Quadrilateral MAOB =360 degrees

so angles AOB and AMB=90 degrees each

angle MBF=90 degrees

M is the midpoint of FA so MA=MF

MB=MF

Triangle MBF is a right triangle because angle BMF is 90 degrees and MB=MF