State whether the following statement is True or False and provide a reason for your answer:
$A$ pair of tangents can be constructed to a circle inclined at an angle of $170^{\circ}$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(A) True.
In a circle,the angle between the two tangents drawn from an external point and the angle subtended by the line segments joining the points of contact to the center are supplementary (i.e.,they add up to $180^{\circ}$).
Let the angle between the tangents be $\theta$ and the angle at the center be $\phi$.
We know that $\theta + \phi = 180^{\circ}$.
Since the angle between the tangents is given as $170^{\circ}$,the angle at the center would be $180^{\circ} - 170^{\circ} = 10^{\circ}$.
Since $10^{\circ} > 0^{\circ}$,it is geometrically possible to construct such a pair of tangents.

Explore More

Similar Questions

Draw a pair of tangents to a circle of radius $5\, cm$ which are inclined to each other at an angle of $60^{\circ}$. Also,provide the justification for the construction.

Difficult
View Solution

Draw a circle with the help of a round bowl turned upside-down. Take a point $P$ in the exterior of the circle and draw tangents to the circle from that point. Write the steps of construction.

Difficult
View Solution

Draw $\odot(O, 4\, cm)$ and a diameter $\overline{PQ}$ in it. Take points $A$ and $B$ such that $A-P-Q$ and $P-Q-B$. From $A$ and $B$,draw tangents to $\odot(O, 4\, cm)$. Write the steps of construction.

Difficult
View Solution

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,provide the justification for the construction and verify the measurement by actual calculation.

Difficult
View Solution

$\odot(P, 4\, cm)$ is given. Construct two tangents to the circle which are perpendicular to each other. Write the steps of construction.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo