Circle Theorems 1 The angle subtended at the

Circle Theorems: 1. The angle subtended at the centre of a circle is twice the angle subtended at the circumference. angle subtended at the centre A B @lhmaths: Lesley Hall

Circle Theorems: 1. The angle subtended at the centre of a circle is twice the angle subtended at the circumference. C A angle subtended at the circumference B @lhmaths: Lesley Hall

Circle Theorems: 1. The angle subtended at the centre of a circle is twice the angle subtended at the circumference. C angle at the centre is twice that at the circumference A B @lhmaths: Lesley Hall

Circle Theorems: 1. The angle subtended at the centre of a circle is twice the angle subtended at the circumference. C x O 2 x A angle at the centre is twice that AOB = 2 x ACB at the circumference B @lhmaths: Lesley Hall

Circle Theorems: 2. Angles subtended by an arc in the same segment of a circle are equal. C x Given: The angle subtended at the centre of a circle is twice the angle subtended at the circumference. 2 x A B @lhmaths: Lesley Hall

Circle Theorems: 2. Angles subtended by an arc in the same segment of a circle are equal. C x D x E x 2 x A B @lhmaths: Lesley Hall

Circle Theorems: 2. Angles subtended by an arc in the same segment of a circle are equal. C x D x ADB = ACB = AEB E x 2 x A B @lhmaths: Lesley Hall

Circle Theorems: 2. Angles subtended by an arc in the same segment of a circle are equal. C x D x A ADB = ACB = AEB E x B @lhmaths: Lesley Hall

Circle Theorems: 2. Angles subtended by an arc in the same segment of a circle are equal. C ADB = ACB = AEB E D angles subtended by by arc AB AB angle subtended arc AB A B @lhmaths: Lesley Hall

Circle Theorems: 2. Angles subtended by an arc in the same segment of a circle are equal. C ADB = ACB = AEB E D angles subtended by by arc AB AB angle subtended in the same segment A B @lhmaths: Lesley Hall

Circle Theorems: 2. Angles subtended by an arc in the same segment of a circle are equal. C ADB = ACB = AEB E D Angles subtended by arc AB in the same segment are equal. A B @lhmaths: Lesley Hall

Circle Theorems: 1 & 2 Examples z 500 x 960 500 Objective: To use theorems 1 and 2 to calculate angles. x = y = 180 – (96 + 50) = 180 – 146 = 340 400 y @lhmaths: Lesley Hall