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