## Tag: circles

### Perpendicular Bisectors of Triangles

What is a perpendicular bisector? A perpendicular bisector of a line segment is a line that makes a 90-degree angle (a right angle) at the midpoint of a segment. In the figure, line b is the perpendicular bisector of line segment AB at C. This implies AC=CB and the measure of the angles at C…

### Tangents to Circles Problems

Problem 1 The figure below shows circle A and rectangle ABCD. The measures of segments are indicated. How long is EB? This problem is not that hard. All you need to see is that AB and AE are radius of Circle A. Also, because ABCD is a rectangle, BD = AC. Now, all you need…

### Proofs of angle in a semicircle theorem

The Angle in a Semicircle Theorem states that the angle subtended by a diameter of a circle at the circumference is a right angle. An alternative statement of the theorem is the angle inscribed in a semicircle is a right angle. Proof Draw a radius of the circle from C. This makes two isosceles triangles….

### Angle inscribed in a semicircle

To solve the two problems below you need to know 1) The area of a circle is Πr2, with r as radius and that the area of a semicircle is of course  half of the circle, ½Πr2 and 2) the theorem the angle  in a semicircle theorem. Problem 1 Prove that the area of the solid…