InterviewSolution
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InterviewSolution
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Seg AB is a diameter of a circle with cente P , seg AC is a chord . A through P and parallel to seg AC intersects the tangent drawn at C is D . Prove that line DB is a tangent to the circle . |
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Answer» In `Delta PAC` , seg `PA cong seg PC " "` …(Radii of the same circle ) ` :. Angle PAC cong angle PCA " "` …(Isosceles Delta theorem ) …(1) seg AC `||` seg PD nd PA is the transversal , ` angle PAC cong angle BPD " " ` ...(Corresponding angles ) ... (2) seg AC `||` seg PD and PC is the transversal , ` angle PCA cong angle CPD " "` ...(ALternate angles ) ...(3) ` :. angle BPD cong angle CPD " "` ... [ From (1) , (2) and (3) ] ...(4) In `Delta BPD and Delta CPD,` seg `BP cong seg CP" "` ...(Radii of the same circle ) ` angle BPD cong angle CPD " " ` ...[ From (4)] seg `PD cong seg PD " "` ...(Common side ) ` :. Delta BPD cong Delta CPD " "` (SAS test) ` :. angle PBD cong angle PCD " " ` ... (c.a.c.t.) ` angle PCD = 90^(@) " "` ... (Tangent is perpendicular to radius ) ` :. angle PBD = 90^(@)` ` :. ` line DB is tangent to the circle at point B ... ( Converse of tangent theorem ) |
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