Question

# Question 5 Draw a line segment AB of length 8 cm. Taking A as center, draw a circle of radius 4 cm and taking B as center, draw another circle of radius 3 cm. Construct tangents to each circle from the center of the other circle.

Solution

## Steps of Construction: Step I: A line segment AB of 8 cm is drawn. Step II: With A as center and radius equal to 4 cm, a circle is drawn which cut the line at point O. Step III: With B as a center and radius equal to 3 cm, a circle is drawn. Step IV: With O as a center and OA as a radius, a circle is drawn which intersect the previous two circles at P, Q, and R, S. Step V: AP, AQ, BR, and BS are joined. Thus, AP, AQ, BR, and BS are the required tangents. Justification: ∠BPA=90∘ (Angle in the semi-circle) ∴AP⊥PB Therefore, BP is the radius of the circle then AP has to be a tangent of the circle.  Similarly, AQ, BR, and BS are tangents of the circle.MathematicsNCERT TextbookStandard X

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