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CBSE Class 10 Answered

Sir/Madam,
In figure, prove that PT is a tangent and PAB is a secant. If PT=6cm, and AB=5cm, then find the leaght of PA. 
By: Shweta.A.Ram
Asked by shweta_aram | 08 Feb, 2016, 03:06: PM
answered-by-expert Expert Answer
PT touches the circle only in one point hence it is a tangent to the circle.
PAB intersects the circle in two distinct points hence it is a secent to the circle.
 
 
Join space OP comma space OA. space Draw space ON space perpendicular space to space AB. Since space perpendicular space from space the space centre space to space the space cord space bisects space the space cord. therefore AN space equals space BN PA. PB space equals space open parentheses PN minus AN close parentheses open parentheses PN plus BN close parentheses space PA. PB equals space open parentheses PN minus AN close parentheses open parentheses PN plus AN close parentheses PA. PB equals PN squared minus AN squared........ left parenthesis 1 right parenthesis PN squared minus AN squared equals PN squared minus open parentheses OA squared minus ON squared close parentheses...... open square brackets increment ONA space is space straight a space right space tiangle comma space AN squared equals OA squared minus ON squared close square brackets PN squared minus AN squared equals PN squared plus ON squared minus OA squared PN squared minus AN squared equals OP squared minus OA squared............. open square brackets increment PNO space is space straight a space right space tiangle comma space OP squared equals ON squared plus PN squared close square brackets PN squared minus AN squared equals OP squared minus OT squared........ open square brackets OT equals OA comma space radii space of space the space circle close square brackets PN squared minus AN squared equals PT squared............. open square brackets increment PTO space is space straight a space right space tiangle comma space OP squared minus OT squared equals PT squared close square brackets......... left parenthesis 2 right parenthesis from space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis space we space get PA. PB space equals space PT squared PA left parenthesis PA plus AB right parenthesis equals PT squared PA left parenthesis PA plus 5 right parenthesis equals 6 squared PA squared plus 5 PA minus 36 equals 0 open parentheses PA plus 9 close parentheses open parentheses PA minus 4 close parentheses equals 0 PA space equals negative 9 space space or space PA space equals 4 PA space is space straight a space distance space and space hence space cannot space be space negative. Hence space PA space equals space 4 cm
Answered by Vijaykumar Wani | 09 Feb, 2016, 11:15: AM

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