Geometry Unit Test

Find the radius of the circumscribed circle of a right triangle if its legs are 10 cm and 24 cm long.

What CANNOT be the length of the third side of a tangential quadrilateral if three sides are 10 cm, 8 cm and 13 cm long?

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Three angles of a cyclic quadrilateral are  $\alpha=38\degree,\ \beta=105\degree\ and\ \delta=75\degree$ What is the measure of angle  $\gamma$  ?

Complete the theorem:

In a circle, if the two endpoints of a ... (A,B) are joined with a third point of the circle, different from A and B, a right-angled triangle is gained the ... of which is the diameter chosen.

Correct the following sentence (write down the sentence without any mistakes):

The inscribed circle of a polygon is the circle that lies inside the polygon and touches all its vertices.

Correct the following sentence (write down the sentence without any mistakes):

A quadrilateral which has an inscribed circle is called a tangential quadrilateral. The sums of the opposite angles of a tangential quadrilateral are equal.

Correct the following sentence (write down the sentence without any mistakes):

The angle bisectors of a triangle are concurrent. The intersection is the centre of the escribed circle of the triangle.

Complete the theorem:

... to a circle from the same external point are congruent.

Complete the theorem:

The sums of the opposite sides of a ... quadrilateral are equal.

Given a point (P) and a circle with radius 6 cm. The distance of the centre of the circle and P is 10 cm. Calculate the length of the tangent segment from P to the circle.

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