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

Answer:

5.1 cm

Step-by-step 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