Theorem 19

Question 1

Theorem

Answer 1

The angke at the centre of a circle standing on a given arc is twice the angle at any point of the circle standing on the same arc.

Question 2

Given

Question 3

Prove

Answer 3

|CAD| =2|

Question 4

Construction

Answer 4

Join B to A and produce to E. Label angles.

Question 5

Proof

Answer 5

[AB] and [AC] are radii of the circle.
=> [AB] =[AC] => triangle ACB is isoceles
=> |<2|=|<3|… Theorem 2
=> |<2|+|<3|= 2|<3|

Also exterier angle |<1|=|<2|+|<3|… Theorem 6
=>|<1|= 2|<3|

Similary |<4|= 2|<5|

Question 6

Corolly 1 of theorem 19

Answer 6

All angkes at points of a circle standing on the same arc are equal.

Given: |<1|=|<2|… QED