The /k/ sound is spelled with <c> or <k> initially, and usually <ck> or <ke> medially or finally. The exceptional spelling <ch> occurs in the loan word Reich, though many English speakers will use a fricative in this word. The /ð/ sound is normally spelled with <th> or <the>.
The contrast is between a voiceless velar stop and a voiced dental fricative. It causes no problems.
The /ð/ sound is one of the rarest sounds in the dictionary, occurring in only 593 words. (Only /ʒ/ with 334 words is rarer.) However, it is very common in transcribed running text, since some of the words using it are the commonest in the language, the, that, these, thus, etc. Apart from these function words, it never occurs initially.
The mean density value is 0.5%. The list makes 31 semantic distinctions, a loading of 65%.
bake bathe baking bathing bakes bathes baker bather bakers bathers blacker blather can than care their cares theirs cat that cats that's cattle that'll cave they've cloak clothe cloaking clothing cloaks clothes Co tho' cow thou cuss thus dicker dither dickered dithered dickering dithering dickers dithers hike Hythe K they kail they'll Ken then key thee keys these kine thine lake lathe lakes lathes like lithe Reich writhe seek seethe seeking seething seeks seethes slicker slither slickers slithers teak teethe tike tithe tikes tithes wick with wicker whither working Worthing wreak wreathe wreaking wreathing wreaks wreathes
John Higgins, Shaftesbury, April 2010.