prove that the tangent at the extermities of a chord of a circle make equal angles with the chord

 

let there be a circle with centre O

let the chord be AB

the tangents from external point p meet the end points of the chord at A and B

so the two tangents are PA and PB

construction- join OP

let OP intersect the chord AB at C

we have to prove that anglePAC = anglePBC

in tringles PCA & PCB,

PA = PB  (tangents from an external point are equal)

angleAPC = angleBPC  (tangents from an external point are equally inclines to OP)

PC = PC  (common)

,

by SAS congr  so,both triangles are congruent to each other

cpct....... anglePAC = anglePBC

thumbs up plz

  • 19

thank you sir!

i will surely try answering most of the questions to help out  others

thanks for your appreciation>>>

  • -11
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