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Question 969326: Hi, can someone help me with this please? Thanks!
Find Bd.
Thanks! Below is a screenshot of the shape. copy and paste the link thanks:).
http://prntscr.com/732xcu
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the length of the radius is 4 + 6 = 10
that the length of AF.
AB and AD are also radii of the same circle.
if they're not already drawn in, then draw them in.
their length is also 10 each.
two right triangles are formed that will help.
triangle BCA and triangle DCA.
the right angle in both triangles is C.
one leg of each right triangle is the length of AC, which is 6, because AC is common to both triangles.
the hypotenuse of each right triangle is the length of AB for triangle BCA and the length of AD for triangle DCA, which are 10 each.
the other leg of each triangle is BC for BCA and CD for DCA.
these will each be the same length because they are they form the base of isosceles triangle BAD.
we'll call the length of each of these x because we don't know what that is right now.
BC and CD. have equal length because the altitude of an isosceles triangle divides the base into two equal segments, those equal segments being BC and CD.
by pythagorus, one leg squared plus the pother leg squared = hypotenuse squared.
for each of these triangles, this becomes 6 square plus x squared = 10 squared which becomes 36 + x^2 = 100.
solve for x^2 to get x^2 = 64
solve for x to get x = 8.
BC and CD are each equal to 8.
BC + CD = BD which is equal to 8 + 8 = 16.
that should be your answer.
BD is equal to 8.
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