Circles
Circle
star_batch_jee_advanced_2025
Grade None
Question:
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:
Step-by-Step Solution
Key Concept: Combine power of a point theorem with proportional segment relationships in circles.
From $(PO)(AO) = (QC)^2$ we get $PO = \frac{9}{2}$. Using the proportion $\frac{QC}{RC} = \frac{PQ}{PR}$ gives $PR = 6$. Then $(RC)^2 = (RB)(RP)$ yields $RB = \frac{8}{3}$.
Correct Answer: 2