A circle touches the sides overline{AB},overl | vedclass

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(C) Let the lengths of the tangents from vertices $A, B, C$ to the circle be $x, y, z$ respectively.Since tangents drawn from an external point to a c

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) Let the lengths of the tangents from vertices $A, B, C$ to the circle be $x, y, z$ respectively.Since tangents drawn from an external point to a circle are equal in length,we have:$AD = AF = x$$BD = BE = y$$CE = CF = z$Given the side lengths of $\Delta ABC$:$AB = x + y = 13$$BC = y + z = 12$$CA = z + x = 5$Adding these three equations:$(x + y) + (y + z) + (z + x) = 13 + 12 + 5$$2(x + y + z) = 30$$x + y + z = 15$We need to find $AD = x$. Using $y + z = 12$:$x + (y + z) = 15$$x + 12 = 15$$x = 15 - 12 = 3$Therefore,$AD = 3$.

$A$ circle touches the sides $\overline{AB}$,$\overline{BC}$,and $\overline{CA}$ of $\Delta ABC$ at the points $D, E, F$ respectively. If $AB=13$,$BC=12$,and $CA=5$,then $AD = \ldots$

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