On the circle below, tangent line BC¯¯¯¯¯ is constructed by striking an arc from point D that intersects circle A at point B. Th
e measure of EC¯¯¯¯¯ is 8 units and other measures are shown on the diagram below. Enter the distance from point D to point B.
1 answer:
Answer:
Step-by-step 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
Where c = AC , a = BD and b = AB
169 = BD² + 25
Subtracting 25 to both sides
169 - 25 = BD²
BD² = 144
Taking square root on both sides
BD = 12 units
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