Plane geometry
angles of an isosceles triangle, the Pythagorean theorem, similar triangles and the ratio of areas of similar figures, the intercept theorem, inscribed and central angles, tangents to a circle, the circumcircle of a right triangle, angles in quadrilaterals, regular polygons, areas of quadrilaterals, area and circumference of a circle, sectors, justifying steps of reasoning
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Compute the length
A circle has radius 18 cm. From a point 30 cm away from its centre a tangent is drawn. How long is the segment from that point to the point of contact?
Choose the side of the triangle
In triangle ABC the angle at vertex C is 22° and the angle at vertex A is 124°. Which side of the triangle is the longest?
Find the distance of the chord from the centre
A chord of a circle of radius 20 cm is 24 cm long. How far from the centre of the circle is the chord?
Give the measure of the angle
From the centre of the circle circumscribed about a regular hexagon every side is seen at the same angle. What is this angle?
Compute the length
A square has a diagonal of 5√2 cm. How long is its side?
Find the length of the segment
In triangle ABC the bisector of angle ACB meets side AB at the point D. |AD| = 15 cm, |DB| = 6 cm, |AC| = 20 cm. How long is the side BC?
Give the measure of the angle
In an isosceles triangle the apex angle measures 110 degrees. What is a base angle?
Compute the area
Two similar figures have their sides in the ratio 7 : 3. The area of the first one is 49 cm². What is the area of the second one?
Compute the length
In a right triangle the hypotenuse is 50 cm and one leg is 48 cm. How long is the other leg?
Compute the length
Two triangles are similar. In the first one two sides are 5 cm and 7 cm. In the second one the side corresponding to the first of them is 20 cm. How long is the side corresponding to the second one?
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