Question
Draw two concentric circles of radii 3cm and 5cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.
✓
Answer
Steps of construction:
1. Draw two concentric circles $C_1, C_2$ of radiü 3 cm and 5 cm respectively taking ' $O$ ' as centre.
2. Draw perpendicular bisector $A B$ of $O T . T$ is any point on $C_2$.
3. Draw circle $C_3$ taking radius $TM = OM$ and M as centre.
4. Circle $C_3$ intersect the circle $C_1$ at $P$ and $Q$. Join $T P$ and $T Q$. These are the required tangents. $T P=T Q=4.1 cm$ by measuring.
Mathematically length of tangent:
Join OP. OP and TP are radius and tangent respectively at contact point P. So, $\angle\text{TPO}=90^\circ.$
By Pythagoras theorem in $\triangle\text{TPO},$
$PT^2= OT^2- OP^2 = 5^2- 3^2 = 25 - 9 = 16$
⇒ PT = 4cm
Difference in measurement and by mathematical calculation
PT = 4.1cm - 4cm = 0.1cm.
1. Draw two concentric circles $C_1, C_2$ of radiü 3 cm and 5 cm respectively taking ' $O$ ' as centre.
2. Draw perpendicular bisector $A B$ of $O T . T$ is any point on $C_2$.
3. Draw circle $C_3$ taking radius $TM = OM$ and M as centre.
4. Circle $C_3$ intersect the circle $C_1$ at $P$ and $Q$. Join $T P$ and $T Q$. These are the required tangents. $T P=T Q=4.1 cm$ by measuring.
Mathematically length of tangent:
Join OP. OP and TP are radius and tangent respectively at contact point P. So, $\angle\text{TPO}=90^\circ.$
By Pythagoras theorem in $\triangle\text{TPO},$
$PT^2= OT^2- OP^2 = 5^2- 3^2 = 25 - 9 = 16$
⇒ PT = 4cm
Difference in measurement and by mathematical calculation
PT = 4.1cm - 4cm = 0.1cm.
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