Question

On the circle below, tangent line BC¯¯¯¯¯ is constructed by striking an arc from point D that intersects circle A at point B. The measure of EC¯¯¯¯¯ is 8 units and other measures are shown on the diagram below. Enter the distance from point D to point B.

Answer 1

`\huge\boxed{BD = 12\ units}`

Explanation:

If AB = 5 , then AE = 5 [Radii of the same circle]

So,

AC = AE + EC

AC = 8+5

AC = 13 units

Now, Using Pythagorean theorem to find the missing side i.e. BD because tangent strikes the circle at 90 degrees making the triangle a right angled triangle

`c^2=a^2+b^2`

Where c = AC , a = BD and b = AB

`13^2 = BD^2+5^2`

169 = BD² + 25

Subtracting 25 to both sides

169 - 25 = BD²

BD² = 144

Taking square root on both sides

BD = 12 units