Hi! It is knew. This one makes sense because knows is <em>present tense</em>, and we are looking for <em>past tense</em>. Known will not fit because "The child <em>known</em> the answer to the question." To me that doesn't seem correct, and seems quite strange. But "The child <em>knew</em> the answer to the question." that seems pretty correct to me, it is in past tense and fits in the sentence.
