Question 2

We will construct the triangle and its circumcircle using perpendicular bisectors.

Step 1 — Draw the base

Let's draw a line segment. We label its endpoints A and B. Its length is 5 cm.

Step 2 — Construct angle A

We place the protractor at point A. We mark an angle of 100°. Let's draw a ray AX from A.

Step 3 — Mark point C

We measure 4 cm along the ray AX. Let's mark point C on this ray. We join point C to point B. This forms $\Delta\text{ABC}$.

Step 4 — Bisect side AB

We open the compass more than half of AB. We draw arcs from A and B. These arcs intersect at two points. Let's draw a line through these points. This line is the perpendicular bisector of AB.

Step 5 — Bisect side AC

We open the compass more than half of AC. We draw arcs from A and C. These arcs intersect at two points. Let's draw a line through these points. This line is the perpendicular bisector of AC.

Step 6 — Find the circumcenter

The two perpendicular bisectors meet. Let's label their intersection point O. Point O is the circumcenter of $\Delta\text{ABC}$.

Step 7 — Draw the circumcircle

We place the compass at point O. We adjust the compass radius to OA. Let's draw a circle. This circle passes through A, B, and C. This is the circumcircle of $\Delta\text{ABC}$.

Step 8 — Determine the center's position

We observe the angle $\angle\text{A}$. $\angle\text{A}$ is 100°. This means $\Delta\text{ABC}$ is an obtuse-angled triangle. The circumcenter of an obtuse triangle lies outside. We can see point O is outside the triangle.

Answer

$\boxed{\text{The centre is outside the triangle.}}$