Question

Consider the diagram of circle A with tangent segments DC and BC. What is the length of DC?

Answer 1

(D) 65 inch

Explanation:

Theorem: Tangents to a Circle from the same point are equal

By this theorem, |DC|=|BC|

`2x^2+15=4x^2-35\\$Collect like terms to solve for x\\15+35=4x^2-2x^2\\2x^2=50\\$Divide both sides by 2\\x^2=25\\x^2=5^2\\$ x=5 inch`

Recall:

`|DC|=2x^2+15`

Substituting x=5 inch into |DC|

`|DC|=2(5)^2+15=2*25+15=50+15\\`

|DC|=65 inch