Shape and Space 2

4 marks · Normal

The diagram shows a circle with centre O. PT is a tangent to the circle at P. OP = 7 cm. Work out the length OT if angle OPT = 60°.

Circle with tangent and radius.

(a)

Find OT.

[3 marks]

(b)

State the property relating the tangent to the radius at P.

[1 mark]

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(a) 14 cm

(b) A tangent meets the radius at 90°.

Show mark scheme and worked solution

Marking points

M1 (a) · 1 mark · Identifies and applies right triangle OPT with OPT = 60° and O = 90°.

A1 (a) · 2 marks · Finds OT = 14 cm correctly (uses trigonometry or Pythagoras, as appropriate).

B1 (b) · 1 mark · States the tangent is perpendicular to the radius at the point of contact.

Worked solution

In right triangle, angle at P = 90°. By sine law: sin(60°) = OP/OT.

A tangent to a circle is perpendicular to the radius at the point of contact.