Take BC midpoint as O, center of circle as radius, and make a circle intersection point AD at two points of MN.

MN is taken as BC vertical line, and the intersection point is JH.

Because the angles BMC and BNC are the angles of the circle, they are 90 degrees.

Because MJ is perpendicular to BC and parallel to AB, MJO angle =90 degrees.

MO=5 MJ=4, so JO=3.

So BJ=2 means AM=2.

Similarly, ND=2 AN= 10-2=8.

2.

I think this method is stupid.

Let the focus of the extension line be n.

According to the valley.

BN Party =2 Party+10 Party =BP Party +PN Party.

BP Party =4 Party +X Party

PN Party =X Party +6 Party

In this paper, two values of the solution of a quadratic equation with one variable about X are introduced.

I didn't count it. Do it yourself

( 1)

△APB∽△DCP .

Ab: (AP -PD)= = AP: DC.

(2)

①△APB∽△PBC. Find PB.

② Pythagorean theorem to find AP. Pay attention to verify the length of CH (ensure that h is on the DC extension line. )