# Exam-Style Question on Geometry

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 550. This question is similar to one that appeared on a GCSE Higher paper in 2019. The use of a calculator is allowed.

The diagram shows a circle with its centre at the origin.

The red line AB is a tangent to the circle at the point B.

Angle OAB is 30°.

Point A has coordinates $$(-10, 0)$$

Point C has coordinates $$(5c, -2c)$$

Find the value of $$c$$ giving your answer correct to three significant figures and showing all of your working.

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