I have a hard circle theorem problem:

The question is here: http://imgur.com/539N56S

Specifically, I want to know why part b) is 60 degrees.

Thanks for any help in advance.

bqrs01
May 1, 2017

#1**+3 **

a.

BAD = 70°

Since BDA has its endpoints on a diameter, it measures 90°

And ABD = 180 - 70 - 90 = 20°

Since BD is a trasnsversal cutting two parallel lines....BDC = ABD.....therefore, BDC = 20°

b.

Note..... BCD is supplemental to BAD = 110°

And angle DBC = 180 - BDC - DCB = 180 - 20 - 110 = 50°

And minor arc DC = 2DBC = 100°

And angle CDT = (1/2) minor arc DC = 50°

And by the experior angle theorem, angle BCD = angle CDT + angle CTD ...so..

BCD = CDT + CTD

110 = 50 + angle CTD .....subtract 50 from both sides

60° = angle CTD = angle BTD

CPhill
May 1, 2017