Question

the lenth of tangent frome a point A at distance 5cm frome tha center of the circle is 4cm find radios

Answer 1

So, Distance of point from centre = √ (r² + l²) , where l is length of tangent.

We can write, 5² = r² + 4²
r² = 25 - 16 = 9
Hence, r = 3cm :)

Answer 2

∵ Radius of a circle is perpendicular to the tangent at the point of contact with the circle

Let the centre ne O

∴ The Δ formed by the radius, tangent and OA will be a right angled Δ 

∴ (radius)² + (tangent)² = (OA)²

or, radius = √{(OA)² - (tangent)²}

                = [√(5)² - (4)²] cm

                = [√25 - 16] cm

                = √9 cm = 3 cm

HOPE IT HELPS......................... :)

If you need the diagram of the figure for reference, then let me know.