Premium Online Home Tutors
3 Tutor System
Starting just at 265/hour
Answer :
Steps to construct the required figure:
Step 1: Draw concentric circles C and C’ of radius 4cm and 6cm respectively and mark the center as O.
Step 2: Mark two points as A and P such that O,A and P lie on the same line.
Step 3:Draw perpendicular bisector of OP which intersects OP at O’.
Step 4: By taking O’ as the center, draw a circle of radius OO’ which intersects the circle C at point T and Q.
Step 5: Now join PT and PQ.
Step 6: PT and PQ are our required tangents whose length is 4.5cm approx.
JUSTIFICATION:
Join OT and OQ,
We have OT ⊥ PT [Radius ⊥ to tangent ]
In the right angled triangle OTP,
\({OP}^2={OT}^2+{PT}^2 \)
\({(6)}^2={(4)}^2+{(PT)}^2 \)
\({PT}^2=36-16=20 \)
\(PT=\sqrt{20}=2\sqrt{5} cm\)
Similarly \(PQ=2\sqrt{5} cm \)
A pair of tangents can be drawn from an external point outside the circle and these tangents have equal length.
\(\therefore \) PT=PQ