Help with circle geometry questions Please! (1 Viewer)

[Amanda92]

Hi, i would really appreciate some help with this question. Thanks


23. Two circles intersect at A and B. The tangent to the first circle at A cuts the second circle at C and the tangent to the second circle at A cuts th first circle at D. prove that tri ABC and tri DBA are similar.

 

[vds700]

Hi, i would really appreciate some help with this question. Thanks


23. Two circles intersect at A and B. The tangent to the first circle at A cuts the second circle at C and the tangent to the second circle at A cuts th first circle at D. prove that tri ABC and tri DBA are similar.

I think what you need to do is use the alternate segment theorem to prove that angleDAB = angleACB and angleCAB = angleADB. Then you can deduce that angleABD = angleABC

Hence the 2 triangles are similar (equiangular)

 

[Drongoski]

Hi, i would really appreciate some help with this question. Thanks


23. Two circles intersect at A and B. The tangent to the first circle at A cuts the second circle at C and the tangent to the second circle at A cuts th first circle at D. prove that tri ABC and tri DBA are similar.

VDS700 is correct. Draw 2 circles to intersect at A and at B. Then draw the 2 tangents. Then in triangles DAB & ACB,
angle DAB = angle ACB (alt segment Thm)
angle ADB = angle CAB (alt segment Thm)
Hence the 3rd angle of tri DAB = 3rd angle of tri ACB
Hence the 2 triangles are equiangular and are therefore similar.