Question

1. b is a point on the circumference of a circle with centre o. ab is a tangent to the circle. oa = 14cm and ob = 3cm calculate the size of angle aob.

Explanation:

Step1: Recall the property of tangent - radius

Since AB is a tangent to the circle with center O and B is the point of tangency, then $\angle ABO = 90^{\circ}$ (tangent - radius property).

Step2: Use cosine function

In right - triangle ABO, $\cos\angle AOB=\frac{OB}{OA}$. Given that $OA = 14$ cm and $OB = 3$ cm, so $\cos\angle AOB=\frac{3}{14}$.

Step3: Find the angle

Then $\angle AOB=\arccos(\frac{3}{14})$. Using a calculator, $\angle AOB\approx77.6^{\circ}$ (rounded to 1 decimal place).

Answer:

$\angle AOB\approx77.6^{\circ}$