Question

Given ab is a tangent of the circle centered at X, ab = 24 , and xd= 5, what is the length of db ?

Answer 1

so since xd is 5 that means ad is 10
now you have 2 sides all you need is to find the last side you can use Pythagorean theorem and get 26 for db
answer 26.

Answer 2

The length of DB is 26.

Explanation:

In figure-1 ,we can see AB is tangent of length 24 and XD is radius of circle of length 5

Since AD is diameter so, it will be calculated as 2*radius = 2* 5 =10

Tangent at any point of circle is perpendicular

so, right triangle ABD at ∠A

In ΔABD

By Pythagoras

hypoteneous² = base² + prependicular²

BD² = AD² + AB²

BD² = 10² + 24²

BD² = 100 + 576

BD² = 676

Taking root booth the sides in above expression,

√( BD)² = √676

BD = 26

Hence, the length of DB is 26.