Thread: Help! 2 questions - triangles and circles

Please help with these two questions.

1) In the figure, two circles touch each other at C. AB is a common tangent touching the circles at A and B and angle ABC is 35 degrees. Find the angle CAB.


2) In the figure, O is the centre of the circle. A and B are two points on the circle so that triangle OAB is an equilateral triangle. OA is produced to C so that OA = AC. Find the angle ABC and prove whether CB is tangent to the circle at B, giving a reason.


Thankyou so much for any help, I don't know where to start in solving these.

Hello, BG5965!

2) In the figure, O is the centre of the circle.
A and B are two points on the circle so that triangle OAB is an equilateral triangle.
OA is produced to C so that OA = AC.
Find the angle ABC and prove whether CB is tangent to the circle at B.

Let , radius
. . Then: .

In

Then: .

Hence: . and is tangent to the circle.


Since , then