In `DeltaABC` with fixed length of `BC` , the internal bisector of angle C meets the side `AB` at `D` and meet the circumcircle at `E.` The maximum value of `CD xx DE` is

Explanation

Since CD is bisector of `angleC`.
`therefore(BD)/(AD)=a/b`
`rArr(AD)/(BD)=b/a`
`rArr(AD+BD)/(BD)=(b+a)/arArrC/(BD)=(a+b)/arArrBD=(ac)/(a+b)`
`AD=(bc)/(a+b)`

Now,
`CD.DE=AD.DB`
`rArrCD.DE=(abc^(2))/((a+b)^(2))`
`rArrCD.DEle(c^(2))/4` `[because(a+b)/2gesqrt(ab)rArr(ab)/((a+b)^(2))le1/4]`