Question

Given a circle with centre O and radius 2.4cm. P is a point such that the lenght of the tengent from Q to the circle is 4.5cm. Find the lenght of OP

Answer 1

5.1 cm

Explanation:

(Probable) Question;

Given a circle with center O and radius 2.4 cm. P is a point on the tangent that touches the circle at point Q, such that the length of the tangent from P to Q is 4.5 cm. Find the length of OP

The given parameters are;

The radius of the circle with enter at O,
`\overline{OQ}` = 2.4 cm

The length of the tangent from P to the circle at point Q,
`\overline{PQ}` = 4.5 cm

The length of OP = Required

By Pythagoras's theorem, we have;

`\overline{OP}`² =
`\overline{OQ}`² +
`\overline{PQ}`²

∴
`\overline{OP}`² = 2.4² + 4.5² = 26.01

`\overline{OP}` = √26.01 = 5.1

The length of OP = 5.1 cm