Question

PLEASE RESPOND ASAP!!!! ITS REALLY IMPORTANT Four tangents are drawn from E to two concentric circles. A, B, C, and D are the points of tangency. Can you name as many pairs of congruent triangles as possible and tell how you can show each pair is congruent?

Answer 1

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:

`(x-h)^2+(y-k)^2=r^2`

Where h and k represent the vertex of the circle and r the radius.

From the figure given we can see that:

`OA=OD,OB=OC,CD=BA`

Since for all the cases we have the same distance .

Assuming that the point on the right is X we can see that :

`\Delta OBX\approx\Delta OCX`

By the SAS (side, angle , side) criteria.

`\Delta OAX\approx\Delta ODX`

For the same criteria SAS (side, angle ,side)

`\Delta BAX\approx\Delta CDX`

For the SSS (side, side,side) criteria