Question

Repeat Exercise $1$ , but work with angle bisectors.

Short answer

The final answer is:

Step-by-step solution

Step 1. Given information:

Perpendicular bisectors of triangle located inside, outside, and on the triangle.

Step 2. Concept used:

We use basic geometric and angle concept.

Step 3. Applying the concept:

Draw an equilateral or an acute triangle ABC.

From three sides of the triangle, draw three perpendicular bisectors.

Thus, all the perpendicular bisectors meet at a point inside the triangle as shown below:

The final answer is:

Step 1. Given information:

Perpendicular bisectors of triangle located inside, outside, and on the triangle.

Step 2. Concept used:

We use basic geometric and angle concept.

Step 3. Applying the concept:

Draw an obtuse triangle (one of the angles is greater than 90 degrees.)

From three sides of the triangle, draw three perpendicular bisectors.

Thus, all the perpendicular bisectors meet at a point outside the triangle as shown below:

The final answer is:

Step 1. Given information:

Perpendicular bisectors of triangle located inside, outside, and on the triangle.

Step 2. Concept used:

We use basic geometric and angle concept.

Step 3. Applying the concept:

Draw a Right-angled triangle (one of the angles is of 90 degrees.)

From three sides of the triangle, draw three perpendicular bisectors.

Thus, all the perpendicular bisectors meet at a point on the triangle. In fact, they meet at a point which lies on the hypotenuse as shown below: