AB and CD are perpendicular diameters of a circle. L is the tangent to the circle at A. M is a variable point on the minor arc AC. The ray BM,DM meet the line L at P and Q respectively. Show that AP⋅AQ=AB⋅PQ.
Show how to construct the point M which givesBQ parallel to DP.
If the lines OP and BQ meet at N find the locus of N.
The lines BP and BQ meet the tangent at D at P′ and Q′ respectively. Find the relation between P′ and Q'.
The lines DP and DQ meet the line BC at P" and Q" respectively. Find the relation between P" and Q".
geometryLocusconstructiontangentdiameter