Question
Write ‘True’ or ‘False’ and justify your answer.
The angle between two tangents to a circle may be 0°.
The angle between two tangents to a circle may be 0°.
✓
Answer
True.
Consider the diameter POQ of a circle with centre O. The tangent at P and Q are drawn, as we know the radius and tangent at contact point are perpendicular so$\angle1=\angle2=90^\circ.$ These are alternate angles so the tangent APB || CQD i.e., angle between two tangent to circle may be zero. Hence, the given statment is true.
Consider the diameter POQ of a circle with centre O. The tangent at P and Q are drawn, as we know the radius and tangent at contact point are perpendicular so$\angle1=\angle2=90^\circ.$ These are alternate angles so the tangent APB || CQD i.e., angle between two tangent to circle may be zero. Hence, the given statment is true.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Write ‘True’ or ‘False’ and justify your answer.
The value of the expression (sin80º - cos80º) is negative.
The value of the expression (sin80º - cos80º) is negative.
D is a point on side QR of $\triangle\text{PQR}$ such that $\text{PD}\perp\text{QR}$ will it be correct to say that $\triangle\text{PQD}\sim\triangle\text{RPD}?$ Why?
→Write the truth value (T/F) of the following statements:
Any two congruent figures are similar.
Any two congruent figures are similar.
It is given that $\triangle\text{DEF}\sim\triangle\text{RPQ}.$ Is it true to say that $\angle\text{D}=\angle\text{R}\text{ and }\angle\text{F}=\angle\text{P}?$ Why?
→State whether the following statements are true or false. Justify your answer.
A circle has its centre at the origin and a point P(5, 0) lies on it. The point Q(6, 8) lies outside the circle.
A circle has its centre at the origin and a point P(5, 0) lies on it. The point Q(6, 8) lies outside the circle.
Write True or False and give reasons for your answer in each of the following.
To construct a triangle similar to a given $\triangle ABC$ with its sides $\frac{7}{3}$ of the corresponding sides of $\triangle ABC$, draw a ray $B X$ making acute angle with $B C$ and $X$ lies on the opposite side of $A$ with respect to $B C$. The points $B_1, B_2, \ldots, B_7$ are located at equal distances on $B X, B_3$ is joined to $C$ and then a line segment $B_6 C^{\prime}$ is drawn parallel to $B_3 C$ where $C^{\prime}$ lies on BC produced. Finally, line segment $A ^{\prime} C ^{\prime}$ is drawn parallel to AC .
→To construct a triangle similar to a given $\triangle ABC$ with its sides $\frac{7}{3}$ of the corresponding sides of $\triangle ABC$, draw a ray $B X$ making acute angle with $B C$ and $X$ lies on the opposite side of $A$ with respect to $B C$. The points $B_1, B_2, \ldots, B_7$ are located at equal distances on $B X, B_3$ is joined to $C$ and then a line segment $B_6 C^{\prime}$ is drawn parallel to $B_3 C$ where $C^{\prime}$ lies on BC produced. Finally, line segment $A ^{\prime} C ^{\prime}$ is drawn parallel to AC .
Write the truth value (T/F) of the following statements:
Any two congruent figures are similar.
Any two congruent figures are similar.
If a quadratic polynomial f(x) is not factorizable into linear factors, then it has no real zero. (True/ False).
Write ‘True’ or ‘False’ and justify your answer.
If a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection.
If a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection.
Write ‘True’ or ‘False’ and justify your answer in the following:
The volume of the frustum of a cone is $\frac{1}{3}\pi\text{h}\big[\text{r}^2_2\ \ \text{r}^2_2-\text{r}^2_2-\text{r}_1\text{r}_2\big],$ where h is vertical height of the frustum and $r_1, r_2$ are the radii of the ends.
→The volume of the frustum of a cone is $\frac{1}{3}\pi\text{h}\big[\text{r}^2_2\ \ \text{r}^2_2-\text{r}^2_2-\text{r}_1\text{r}_2\big],$ where h is vertical height of the frustum and $r_1, r_2$ are the radii of the ends.