For this problem we have four tangents drawn from E to two concentric circles. A,B,C and D represent points of tangency, and we need to identify all the possible congruent triangles.
The hint for this case is use the equation of a circle given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where h and k represent the vertex of the circle and r the radius.
From the figure given we can see that:
[tex]OA=OD,OB=OC,CD=BA[/tex]
Since for all the cases we have the same distance .
Assuming that the point on the right is X we can see that :
[tex]\Delta OBX\approx\Delta OCX[/tex]
By the SAS (side, angle , side) criteria.
[tex]\Delta OAX\approx\Delta ODX[/tex]
For the same criteria SAS (side, angle ,side)
[tex]\Delta BAX\approx\Delta CDX[/tex]
For the SSS (side, side,side) criteria
