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Let \( O \) be the center of a circle with radius 4. Suppose that \( DL \) and \( DQ \) are tangent to circle \( O \) at points \( L \) and \( Q \) respectively. If \( DL = 3 \), find the area of quadrilateral \( DLOQ \).

Answer :

Triangles DLO and DQO are right triangles, each with one leg of length 3 (the tangent length) and one leg of length 4 (the radius). Since the area of each of these triangles is half the product of the leg lengths, their area together is the product of the leg lengths:

... (3 units)×(4 units) = 12 square units

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