Question
Download Solution PDFIn the given figure a point P outside the circle a secant is drawn that cuts the circle at B and A and another secant is drawn that pass through the centre of circle and cuts it at D and C if PB = 8, AB = 12 and OP = 18 then find the radius of circle.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
AB = 12, PB = 8, and OP = 18
⇒ PA = AB + PB
⇒ PA = 8 + 12
⇒ PA = 20
⇒ PD = 18 - r
⇒ PC = 18 + r
Where, r = radius of circle
Formula Used:
In two chords AB and CD intersect at outer point of P then,
PB × PA = PD × PC
Calculation:
PB × PA = PD × PC
⇒ 8 × 20 = (18 - r)(18 + r)
⇒ 160 = 182 - r2
⇒ r2 = 324 - 160
⇒ r2 = 164
⇒ r =
⇒ r =
∴ The radius of circle is
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