Question

6. AB and BC are both tangents to the circle centre O (left).

If OA = 5 cm and AB = 12 cm calculate:
a) the size of angle OAB,
b) the length OB.
7. If OA is a radius of the circle (below) and PB the tangent to
the circle at A, calculate angle ABO.

Answer 1

a) The size of angle OAB is 90°.

b) The length of O is 13cm.

7. Angle ABO is 28°.

Explanation:

A) It is a right angle.

B) Since A is a right angle I can use the Pythagorean Theorem.

`12^(2)+5^(2)=c^(2)`

144+ 25=
`c^(2)`

`√(169)=\sqrt x^(2)`

x=13

7) Since Angle OAB is a right angle and all interior angles of a shape equal 180° I added 90 and 62 and subtracted the sum by 180.

90+62=152

180-152=28