Question

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

Answer 1

Answer:

(D) 65 inch

Step-by-step 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