12) A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle.
Show that the minimum length of the hypotenuse is
It is given that
A point on the hypotenuse of a triangle is at a distance a and b from the sides of the triangle
Let the angle between AC and BC is
So, the angle between AD and ED is also
Now,
CD =
And
AD =
AC = H = AD + CD
= +
Now,
When
Hence, is the point of minima
and
AC = =
Hence proved