As shown in the figure, D is a point in the quadrilateral aebc, connecting AD and BD. it is known that Ca = CB, Da = dB and EA = EB. (1) are the three points c, D and E in a straight line? Why? (2) If AB = 24, ad = 13, CA = 20, what is the length of CD?

As shown in the figure, D is a point in the quadrilateral aebc, connecting AD and BD. it is known that Ca = CB, Da = dB and EA = EB. (1) are the three points c, D and E in a straight line? Why? (2) If AB = 24, ad = 13, CA = 20, what is the length of CD?

(1) Reason: link cd.ed, in △ ADC and △ BDC, AC = bcad = bdcd = CD, AC = bcad = bdcd = CD, AC = bcad = bcad in △ ADC and △ BDC, AC = bcad = bcad in △ ADC and △ BDC, AC = BCD, AC = BCD, AC = bcad = bcad in △ ADC and △ BDC, AC = bcad in △ ADC and △ BDC, AC = bcad = BDAE = bed = ed, in △ ade and △ ADC and △ ADC and △ ADC 8780; ≌ △ bdcd (bdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdcdit's not easy+ (2) connect AB, ∵ AC = BC, ∵ ACD = ∵ BCD, ∵ AF = BF = 12ab, CF ⊥ ab. ∵ AB = 24, ∵ AF = 12. ∵ ad = 13, CA = 20, ∵ in RT △ ADF and △ AFC, we get FD = 5, FC = 16, ∵ CD = 16-5 = 11 by Pythagorean theorem