Question

In each triangle p is the circumcenter use circumcenter theorem to solve for the givin values

Answer 1

The measure of BP and AB is 12 and 22 respectively.

Explanation:

Circumcenter theorem states that the vertices of a triangle are equidistant from the circumcenter.

Since p is the circumcenter that means PA=PB=PC.

Now, from the figure, it is given that PC=12 and PC is also equal to PB, thus the measure of PB=12.

Let OP be the perpendicular on AB.

Now, also from the figure, it is given that AO=OB=11, and AB=AO+OP, therefore

AB=11+11=22.

Thus, the measure of BP and AB is 12 and 22 respectively.

Answer 2

Circumcenter theorem states that the vertices of the each triangle are equidistant from the circumcenter.

As per the statement:

It is given that: P is the circumference

From the given figure:

CP = 12 units.

then;

by circumcenter theorem;

AP= BP =CP = 12 units.

Next find the value of AB:

Labelled the diagram:

AD = 11 units

then;

AB = AD+DB

Since: AD=DB [You can see it from the given figure]

then;

AB = 2AD = 2(11) = 22 units

Therefore, the value of BP and AB are: 12 units and 22 units