Circle Theorems Question help

Hi guys,

My maths GCSE exam is in 4 weeks from now. Ive been revising but i struggle on circle theorems. I was looking for some questions and i came across some questions which ive put in the attachment, i don't remember them exactly as they were so i have made up some of the figures. Please can someone show me how to work these out so that i can practice it.
I will really appreciate any help. This is really important for me to learn and i will be grateful for any working out.
The attachment has 2 questions with it.

Thank you in advance.

1. Note that angle ABC=90 degrees (angle in a semi-circle)

2. triangle ABC is isosceles so what is angle ABC ?
angle XBZ=angle ABC (vertically opposite angles.

Thank for your help
however im still unsure about the 1st one i understand number 2. For 1 do we use cosine rule to find the length of the diameter?

No. Pythagoras. ABC is a right angled triangle.

Hi guys,

My maths GCSE exam is in 4 weeks from now. Ive been revising but i struggle on circle theorems. I was looking for some questions and i came across some questions which ive put in the attachment, i don't remember them exactly as they were so i have made up some of the figures. Please can someone show me how to work these out so that i can practice it.
I will really appreciate any help. This is really important for me to learn and i will be grateful for any working out.
The attachment has 2 questions with it.

Thank you in advance.