In the figure, chords AE and BC intersect each other at point D. (i) If` `∠`CDE = 90°, AB = 5 cm, BD = 4 cm and CD = 9 cm Find DE. (ii) If AD = BD, show that AE = BC
Join AB. i) In Rt. ΔADB, `AB ^2 = AD^2 + DB^2` `5^2 = AD ^2 + 4^2` `AD^2 = 25 - 16` `AD^2 9` AD = 3 Chords AE and CB intersect each other at D inside the circle AD x DE = BD x DC 3 × DE = 4 × 9 DE = 12 cm ii) If AD = BD .......(i) We know that: AD × DE = BD × DC But AD = BD Therefore, DE = DC .......(ii) Adding (i) and (ii) AD + DE = BD + DC Therefore, AE = BC
Solution In the Figure, Chords Ae and Bc Intersect Each Other at Point D. (I) If` `∠`Cde = 90°, Ab = 5 Cm, Bd = 4 Cm and Cd = 9 Cm Find De. (Ii) If Ad = Bd, Show that Ae = Bc Concept: Chord Properties - a Straight Line Drawn from the Center of a Circle to Bisect a Chord Which is Not a Diameter is at Right Angles to the Chord.