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Answer:1. A circle with radius 6 cm is drawn taking O as centre2. Point P is marked at 10 cm away from centre of circle.3. With the half of compass mark M which is the midpoint of OP.4. Draw a circle with centre M, taking radius MO or MP which intersects the given circle at Q and R.5. Now join PQ and PR. These are the tangents of the circle.We know that, the tangent to a circle is perpendicular to the radius through the point of contact.∴ In △OPQ, OQ⊥QPand in △OPR, OR⊥PRHence, both △OPQ and △OPR are right angle triangles.Applying Pythagoras theorem to both △s, we get:OP 2 =OQ 2 +PQ 2 and OP 2 =OR 2 +PR 2 OQ=OR=radius=6 cm and OP=10 cm∴ 10 2 =6 2 +PQ 2 and 10 2 =6 2 +PR 2 ⇒PQ 2 =100−36=64and PR 2 =100−36=64∴ PQ=PR=8 cmHence, the length of the tangents to a circle of radius 6 cm, from a point 10 cm away from the centre of the circle, is 8 cm

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