Angles and Tangents of Circles

In the diagram on the right, ABC is a straight line and O is the centre of the circle. Given that AB = OB and ∠BAO = 28°, calculate the value of x.

The diagram on the right shows a circle with centre O. Given that OQS is an equilateral triangle and PQR is a tangent to the circle, calculate the value of x.

The diagram on the right shows a circle with centre O. Given that OQS is an equilateral triangle and PQR is a tangent to the circle, calculate the value of y.

The diagram on the right shows a circle with centre O. Given that OQS is an equilateral triangle and PQR is a tangent to the circle, calculate the value of z.

In the diagram on the right, O is the centre of the circle and PQR is a tangent to the circle. Given that QT = ST and ∠QTS = 48°, calculate the value of x.

In the diagram on the right, O is the centre of the circle and PQR is a tangent to the circle. Given that QT = ST and ∠QTS = 48°, calculate the value of y.

In the diagram on the right, O is the centre of the circle and PQR is a tangent to the circle. Given that QT = ST and ∠QTS = 48°, calculate the value of z.

The diagram on the right shows a circle of radius 5 cm centred at O. Given that PQ and PR are tangents to the circle and ∠QSR=60∘ Calculate the value of x.

The diagram on the right shows a circle of radius 5 cm centred at O. Given that PQ and PR are tangents to the circle and ∠QSR=60∘ Calculate the value of PQ.

In the diagram on the right, O is the centre of the circle with radius 3 cm and ROS is a straight line. Given that ∠ORP=25 and PS is a tangent to the circle, calculate the value of x.