plz help.

1. To find the circumradius of a triangle with side lengths 29, 29, and 40, we can use the formula:

R = abc / (4A)

where R is the circumradius, a, b, and c are the side lengths of the triangle, and A is the area of the triangle.

First, we need to find the area of the triangle. We can use Heron's formula:

s = (a + b + c) / 2

A = sqrt(s(s-a)(s-b)(s-c))

where s is the semiperimeter of the triangle.

In this case, a = b = 29 and c = 40. Therefore, s = (29 + 29 + 40) / 2 = 49.

A = sqrt(49(49-29)(49-29)(49-40)) = 420

Now we can use the formula for the circumradius:

R = abc / (4A) = (29)(29)(40) / (4(420)) = 29/6

So the circumradius of the triangle is 29/6.

2. Let's start by drawing a diagram of the triangle PQR:

```
        P
       / \
      /   \
     /     \
    /       \
   /         \
  /           \
 Q-------------R
```

Since M is the midpoint of PQ, we can label PM and MQ as 18 each (half of 36). Let X be the point on QR such that PX bisects angle QPR, as shown:

```
        P
       / \
      /   \
     /     \
    /       \
   /    X    \
  /-----------\
 Q---------Y---R
```

Since PX bisects angle QPR, we have:

angle QPX = angle RPY

Therefore, triangles QPX and RPY are similar, and we can use their side lengths to find the length of PY.

Since M is the midpoint of PQ, we have:

PM = MQ = 18

Since PX bisects angle QPR, we have:

angle QPX = angle RPY

Therefore, triangles QPX and RPY are similar, and we have:

PX / RY = QX / PY

We can solve for PY to get:

PY = (QX * RY) / PX

We can use the Pythagorean theorem to find QX and RY:

QX^2 + PX^2 = PQ^2

RY^2 + PY^2 = PR^2

Substituting for QX and RY, we get:

((PQ - PX) / 2)^2 + PX^2 = PQ^2

PY^2 + ((PR - PY) / 2)^2 = PR^2

Simplifying each equation, we get:

5PX^2 - 2PQ * PX + PQ^2 = 0

5PY^2 - 2PR * PY + PR^2 = 0

Using the quadratic formula to solve for PX and PY, we get:

PX = PQ / 5 = 36 / 5

PY = PR / 5 = 22 / 5

Now we can use the fact that MY = 8 to find the length of RY:

RY^2 + MY^2 = MR^2

RY^2 = MR^2 - MY^2

RY^2 = (PR / 2)^2 - 8^2

RY^2 = 225

RY = 15

Finally, we can use the formula for the area of a triangle:

A = (1/2) * base * height

to find the area of triangle PYR:

A = (1/2) * PY * RY = (1/2) * (22/5) * 15 = 33

So the area of triangle PYR is 33.

3. It is not clear what is meant by "find bc a". Please provide more information or clarification.

3. By the angle bisector theorem,  BC = 22/5 and BZ = 10/3.

Acute isosceles triangle.

Sides: a = 29   b = 29   c = 40

Area: T = 420
Perimeter: p = 98
Semi-perimeter: s = 49

Circumradius = [abc] / 4T =33,640 / 1,680 =841 / 42 = 20.0238