SOLUTION: In the diagram shown in the image, ⊙A is tangent to ⊙C, and BD is tangent to ⊙A. The radius of ⊙A is 7 meters, and the radius of ⊙C is 4 meters. What is the area, to the

Algebra ->  Circles -> SOLUTION: In the diagram shown in the image, ⊙A is tangent to ⊙C, and BD is tangent to ⊙A. The radius of ⊙A is 7 meters, and the radius of ⊙C is 4 meters. What is the area, to the       Log On


   

Question 1183546: In the diagram shown in the image, ⊙A is tangent to ⊙C, and BD is tangent to ⊙A. The radius of ⊙A is 7 meters, and the radius of ⊙C is 4 meters. What is the area, to the nearest square centimeter, of △ADB? Here is a link to the image: https://imgur.com/a/WQnYGaB
Answer by ikleyn(52914) About Me  (Show Source):
You can put this solution on YOUR website!
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In the diagram shown in the image, ⊙A is tangent to ⊙C, and BD is tangent to ⊙A.
The radius of ⊙A is 7 meters, and the radius of ⊙C is 4 meters.
What is the area, to the nearest square centimeter, of △ADB?
Here is a link to the image: https://imgur.com/a/WQnYGaB
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Triangle ADB is a right-angled triangle.


Its leg AB has the length of 7 meters;  its hypotenuse is  AD = 7 + 4 + 4 = 15 meters.


HENCE, its other leg is  sqrt%2815%5E2+-+7%5E2%29 = sqrt%28225-49%29 = sqrt%28176%29 = 4%2Asqrt%2811%29.


The area of this right-angled triangle is half the product of its legs


    area = %281%2F2%29%2A7%2A4%2Asqrt%2811%29 = 7%2A2%2Asqrt%2811%29 = 14%2Asqrt%2811%29 = 46.43274706 square meters.    ANSWER

Solved and explained.