Circles
Tangent to Circles
Grade 11
Question:
<p>In a circle with centre 'O' PA and PB are two chords. PC is the chord that bisects the angle APB. The tangent to the circle at C is drawn meeting PA and PB extended at Q and R respectively. If QC = 3, QA = 2 and RC = 4, then length of RB equals:</p>
<p>(a) 2</p>
<p>(b) \(\frac{8}{3}\)</p>
<p>(c) \(\frac{10}{3}\)</p>
<p>(d) \(\frac{11}{3}\)</p>
Step-by-Step Solution
Key Concept: Apply tangent properties and angle bisector theorem along with tangent-secant power relationships.
<p>Use the property that tangent from an external point to a circle has equal length property and angle bisector theorem. By tangent-secant relationships and the angle bisector property of chord PC, we can establish that RB = \(\frac{10}{3}\).</p>
Correct Answer: C