Lengths in Circles

Lesson

Practice

Lesson

We may be asked to find different values within a circle, such as an angle or a chord length. We can use all our existing mathematical knowledge, including the properties of triangles and quadrilaterals, Pythagoras' theorem, as well as congruency proofs to find certain these values.

Recap of Congruency Proofs

SAS- two pairs of equal corresponding sides and the included angle is equal.
AAS- two pairs equal corresponding angles, and a pair of equal corresponding sides.
SSS- three pairs of equal corresponding sides.
RHS- right-angled triangles, with equal hypotenuses and a pair of equal corresponding sides.

Now let's look at how we can use these geometrical principles by looking at some examples.

Worked Examples

Question 1

$C$C is the centre of the circle. Calculate $x$x, giving a reason related to the properties in a circle for your answer.

Question 2

What is the value of $x$x? Give reasons.

Question 3

Calculate $x$x, the length of a chord in the circle with centre $O$O. In your answer, give reasons related to the properties in a circle.

Outcomes

9.G.C.3

The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. Angles in the same segment of a circle are equal. if a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle. The sum of the either pair of the opposite angles of a cyclic quadrilateral is 180 degree and its converse.