O is the center of a circle of radius 8cm. The tangent at a point A on the circle cuts a line through O at B such that AB = 15 cm. Find OB
Consider a circle with center O and radius OA = 8cm = r, AB = 15 cm.
(AB) tangent is drawn at A (point of contact)
At point of contact, we know that radius and tangent are perpendicular.
In ΔOAB, ∠OAB = 90°, By Pythagoras theorem
𝑂𝐵2 = 𝑂𝐴2 + 𝐴𝐵2
`OB = sqrt(8^2 + 15^2)`
= 17 cm
∴ 𝑂𝐵 = 17 𝑐𝑚