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.
If $cosA + cos^2A = 1, then sin^2A + sin^4A = 1$
→If $cosA + cos^2A = 1, then sin^2A + sin^4A = 1$
Every odd integer is of the form 2m - 1, where m is an integer (True/ False).
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?
→Write ‘True’ or ‘False’ and justify your answer.
The length of tangent from an external point on a circle is always greater than the radius of the circle.
The length of tangent from an external point on a circle is always greater than the radius of the circle.
State whether the following statements are true or false. Justify your answer.
$\triangle\text{ABC}$ with vertices A(-2, 0), B(2, 0) and C(0, 2) is similar to $\triangle\text{DEF}$ with vertices D(-4, 0) and F(0, 4).
→$\triangle\text{ABC}$ with vertices A(-2, 0), B(2, 0) and C(0, 2) is similar to $\triangle\text{DEF}$ with vertices D(-4, 0) and F(0, 4).
Write the truth value (T/F) of the following statements:
Two polygons are similar, if their corresponding angles are proportional.
Two polygons are similar, if their corresponding angles are proportional.
A and B are respectively the points on the sides PQ and PR of a triangle PQR such that PQ = 12.5cm, PA = 5cm, BR= 6cm and PB = 4cm. Is AB || QR? Give reasons for your answer.
Two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Are the two triangles similar? Why?
The product of any three consecutive natural number is divisible by 6 (True/ False).
If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2r, then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle. Is this statement false Why?