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### High School Mathematics - 28.10 Construction of a Tangent from an External Point Without Using the Centre

 Step 1: Draw a secant PAB to the circle. Step 2: Bisect PB. Let M be the midpoint of PB. Step 3: Taking M as centre and MP as radius draw a semicircle. Step 4: Draw a line perpendicular to PB through A. Let it intersect the semicircle at point C. Step 5: Taking P as centre and PC as radius, draw arcs to the given circle at two points say Q and R. Step 6: Join PQ and QR. PQ and QR are the required tangents. Directions: Construct tangents to the following.
 Q 1: To a circle of radius 5 cms, draw a tangent without using the centre.Answer: Q 2: Answer: Q 3: Answer: Q 4: Answer: Q 5: To a circle of radius 4.5 cms, draw a tangent without using the centre.Answer: Q 6: Answer: Q 7: To a circle of radius 3.5 cms, draw a tangent without using the centre.Answer: Q 8: To a circle of radius 8 cms, draw a tangent without using the centre.Answer: Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!

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