(a) Name the radii _____________. Name the tangents ________________.(b) If given that AC is 6 cm and AE is 14, what is DE? Show all work or no credit.Answer:

Answer:Part a) The radii are AC and AD and the tangents are CE and DEPart b) [tex]DE=4\sqrt{10}\ cm[/tex]Step-by-step explanation:Part a) we know thatThe radius of a circle is the distance from the center of the circle to any point on the circleA tangent to a circle is a straight line which touches the circle at only one pointsoIn this problemThe radii are AC and ADThe tangents are CE and DEPart b) If given that AC is 6 cm and AE is 14, what is DE?we know thatThe triangle ADE is a right triangle , because the radius AD is perpendicular to the tangent DEApplying the Pythagoras Theorem[tex]AE^{2}= AD^{2}+DE^{2}[/tex]we have[tex]AD=AC=6\ cm[/tex] -----> is the radius of the circle[tex]AE=14\ cm[/tex]substitute and solve for DE[tex]14^{2}= 6^{2}+DE^{2}[/tex][tex]DE^{2}=196-36[/tex][tex]DE^{2}=160[/tex][tex]DE=\sqrt{160}=4\sqrt{10}\ cm[/tex]