Question:
how to construct a tangent to a circle without using its center
Answer:
Construction:
1. Draw a secant PAB to the circle.
2. PB is bisected at M.
3. Take M as a centre and PM as a radius, a semicircle is drawn.
4. Now from point A, draw perpendicular to AB which intersect the semicircle at C.
5. Take P as center and PC as radius, arcs are drawn to intersect the given circle at Q and R.
6. Now join PQ and PR.
7. So PQ and PR the required tangents.
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