Identifying the centre of a circle

Question

I've been asked to identify with reasons of properties of circles , the centre of the circle which passes through

Q1 . A, D and E

Q2. A, C, And E .

I'm not too sure how to approach this question

Answer 1

Like Lee Mosher hinted, finding the angles will help you solve both questions. I'll provide a couple of hints which should hopefully give you an idea on how to approach both questions.

$FA = FC$ since they're both tangents drawn from $F$ to the circle.

$\implies \angle FCA = \angle FAC \implies \angle BAC = 26^o \implies \angle DAE = 90^o$. (This is should be enough to solve Q1)

Another hint: Join $B$ to $D$ and compare $\angle ADB$ and $\angle ACB$, and $\angle CAB$ and $\angle CDB$.