Coaching Centre
Intersecting chords, secants and tangents
Products of intercepts for intersecting chords, two secants from an external point, and a secant and a tangent (the square of the tangent).
Products of intercepts
Chords cross at $P$ with $AP = 4$, $PB = 6$ and $CP = 3$. Find $PD$.
From $P$, a secant meets the circle at $A$ and $B$ with $PA = 4$ and $PB = 9$. Find the tangent length $PT$.
Chords cross: $AP = 4$, $PB = 6$, $CP = 3$. Find $PD$.
$24 = 3 \times PD$.
Secant: $PA = 4$, $PB = 9$. Tangent length?
$\sqrt{36}$.
Two secants: $PA = 3$, $PB = 12$, $PC = 4$. Find $PD$.
$36 = 4 \times PD$.
Chords: $AP = 10$, $PB = 2$, $CP = 4$. Find $PD$.
$20 = 4 \times PD$.
Tangent $PT = 8$, $PA = 4$. Find $PB$.
$64 = 4 \times PB$.
Using the previous question, find the chord length $AB$.
$16 - 4$.
Chords cross with $AP = x$, $PB = x$, $CP = 2$, $PD = 8$. Find $x$.
$x^2 = 16$.
Secant $PA = 5$, chord $AB = 15$. Tangent length $PT$?
$PB = 20$; $PT^2 = 100$.
New numbers every time. Keep going until you get five in a row.