Q10 of 805 Page 13

Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also, verify the measurement by actual calculation.


Steps of Construction:


1. Draw two concentric circles C1 and C2 with common center O and radius 4 cm and 6 cm.



2. Take any point P on the outer circle C2 and join OP.



3. Draw bisector of OP which bisects OP at M.



4. Taking M as center and OM as radius, draw a dotted circle which cuts the inner circle C1 at two points Q and R.



5. Join PQ and PR. PQ and PR are the required tangents.



On measuring PQ and PR,


⇒ PQ = PR = 4.4 cm


By calculation:


In Δ OQP, ∠ OQP = 90°


By Pythagoras Theorem,


⇒ OP2 = OQ2 + PQ2


⇒ PQ2 = 62 – 42 = 36 – 16 = 20


⇒ PQ = √20 = 4.4 cm


Hence, verified.


More from this chapter

All 805 →
8

Write the steps of construction for drawing a pair of tangents to a circle of radius 3 cm, which are inclined to each other at an angle of 60°.

 9

Draw a circle of radius 3 cm. Draw a tangent to the circle making an angle of 30° with a line passing through the centre.

HINT: Draw a circle with centre O and radius 3 cm. Draw a radius OA and produce it to B. Make ∠AOP = 60o. Draw PQ ⊥ OP, meeting OB at Q. Then, PQ is the desired tangent such that ∠OQP = 30°.



 1

Draw a line segment AB of length 5.4 cm. Divide it into six equal parts. Write the steps of construction.

 2

Draw a line segment AB of length 6.5 cm and divide it in the ratio 4 : 7. Measure each of the two parts.