Circles
Tangent properties
Grade 11
Question:
<p>AC is diameter of circle. AB is a tangent. BC meets the circle again at D. AC = 1, AB = a, CD = b, then:</p>
<p>(a) ab > 1</p>
<p>(b) ab < 1</p>
<p>(c) \frac{b}{a} > \frac{1}{2√(1 + \frac{a²}{2})}</p>
<p>(d) \frac{b}{a} < \frac{1}{2√(1 + \frac{a²}{2})}</p>
Step-by-Step Solution
Key Concept: Apply tangent properties and power of point to relate the segments.
<p>Using properties of tangents and the power of a point theorem, along with the constraint that AC is a diameter and AB is tangent at A.</p>
Correct Answer: B, C