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CBSE Class 10 Answered

In the figure a tangent and a line segment PBA is drawn to a circle with centre O. If OL is perpendicular to AB, prove that PA*PB=PT^2
Asked by Abha | 14 Feb, 2016, 01:48: PM
answered-by-expert Expert Answer
OL space is space perpendicular space to space chord space AB. straight A space perpendicular space drawn space from space the space centre space bisects space the space chord. So space AL space equals space BL In space increment POL PA space cross times PB space equals open parentheses space PL plus AL close parentheses open parentheses space PL minus BL close parentheses PA space cross times PB space equals open parentheses space PL plus BL close parentheses open parentheses space PL minus BL close parentheses space space space space space space space space space space space space space space space space space space space left square bracket Since space AL space equals space BL right square bracket PA space cross times PB space equals space PL squared minus BL squared............. left parenthesis 1 right parenthesis space PL squared minus BL squared space equals space space PL squared minus open parentheses OB squared minus OL squared close parentheses space space space space space space space space space space space space space space space space space space space space space left square bracket Using space Pythagoras space theorem space in space increment OLB right square bracket space PL squared minus BL squared space equals space space PL squared plus OL squared minus OB squared space space space PL squared minus BL squared space equals space space PL squared plus OL squared minus OT squared space space space space space space space space space space space space space space space space space space space space space space space left square bracket Radii space of space circle space OT space equals space OB right square bracket space PL squared minus BL squared space equals space space OP squared minus OT squared space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left square bracket Using space Pythagoras space theorem space in space increment OPL right square bracket space PL squared minus BL squared space equals space space PT squared space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left square bracket Using space Pythagoras space theorem space in space increment OPT right square bracket....... left parenthesis 2 right parenthesis From space left parenthesis 1 right parenthesis space space and space left parenthesis 2 right parenthesis space we space get PA space cross times PB space equals space PT squared space space space
Answered by Vijaykumar Wani | 15 Feb, 2016, 12:11: PM

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