Angle in a Semicircle Is 90 Degrees

Q. AB is a chord of a circle with centre O, AOC is a diameter and AT is the tangent at A as shown in Figure. Prove that $\angle BAT=\angle ACB$.

Q. Question 4
In the given figure, if $x+y=w+z,$ then prove that AOB is a line.

Q. A Circle is inscribed in triangle ABC having sides 8 cm, 10 cm, and 12 cm as shown in the given figure. Find AD?

1. 2.5 cm
2. 3 cm
3. 5 cm
4. 4 cm

Q. The angle in a semicircle is ___.

1. acute angle
2. obtuse angle
3. right angle
4. any of the above

Q.

AB is the longest chord of a circle with centre O. P is any point on the circumference of the circle, not coinciding with A or B. Find the angle $\angle$APB in degrees.

__

Q.

The angle subtended by the diameter of a circle is

1. 180 degrees

2. 90 degrees

3. 60 degrees

4. 45 degrees

Q.

Identify the following parts of a circle in the adjoining figure : Centre point

Q. AB is the longest chord of a circle with centre O. P is any point on the circumference of the circle, not coinciding with A or B. Find $\angle APB$ in degrees.

1. 90${}^{\circ }$
2. 80${}^{\circ }$
3. 75${}^{\circ }$
4. 100${}^{\circ }$

Q. In Fig. 8.64, PA and PB are tangents from an external point P to a circle with centre O. LN touches the circle at M. Prove that PL+ML=PN+MN.

Q. P is a point on a circle whose longest chord is AB. If P doesn't coincide with A or B, then $\angle APB=$ .

1. 90${}^{\circ }$
2. 100${}^{\circ }$
3. 80${}^{\circ }$
4. 75${}^{\circ }$

Q. AB is the longest chord of a circle with centre O. P is any point on the circumference of the circle, not coinciding with A or B. Find $\angle APB$ in degrees.

1. 75 degrees
2. 90 degrees
3. 100 degrees
4. 80 degrees

Q.

In fig., a circle is inscribed in a triangle ABC having side BC = 8 cm, AC = 10 cm and AB = 12 cm. Find AD, BE and CF. [3 MARKS]

Q. The circle described on any focal chord of a parabola as diameter touches the directrix.

1. True
2. False

Q.

AB is the longest chord of a circle with centre O. P is any point on the circumference of the circle, not coinciding with A or B. Find the angle $\angle$APB in degrees.

__

Q. In the given circle, O is the centre and AD, AE are the two tangents. If BC is also a tangent, then prove that 2AE = AB + BC + AC

Q.

AB is the longest chord of a circle with centre O. P is any point on the circumference of the circle, not coinciding with A or B. Find the angle $\angle$APB in degrees.

__

Q.

In fig., a circle is inscribed in a triangle ABC having side BC = 8 cm, AC = 10 cm and AB = 12 cm. Find AD, BE and CF. [3 MARKS]

Q.

AB is the longest chord of a circle with centre O. P is any point on the circumference of the circle, not coinciding with A or B. Find $\angle APB$ in degrees.

1. 90 degrees

2. 100 degrees

3. 80 degrees

4. 75 degrees

Q. P is a point on a circle whose longest chord is AB. If P doesn't coincide with A or B, then $\angle APB=$ .

1. 90${}^{\circ }$
2. 100${}^{\circ }$
3. 80${}^{\circ }$
4. 75${}^{\circ }$

Q.

Question 2
Draw a right $\Delta$ABC in which BC = 12 cm AB = 5 cm and $\angle B={90}^{\circ }$ Construct a triangle similar to it and of scale factor $\frac{2}{3}$. Is the new triangle also a right triangle?
Thinking process
Here scale factor $\frac{m}{n}=\frac{2}{3}$ i.e m < n then the triangle to be constructed smaller than the given triangle Use this concept and then construct the required triangle.

Q.

AB is the longest chord of a circle with centre O. P is any point on the circumference of the circle, not coinciding with A or B. Find the angle $\angle$APB in degrees.

__

Q. AB is the longest chord of a circle with centre O. P is any point on the circumference of the circle, not coinciding with A or B. Find $\angle APB$ in degrees.

1. 75${}^{\circ }$
2. 90${}^{\circ }$
3. 100${}^{\circ }$
4. 80${}^{\circ }$

Q. The angle in a semicircle is ___.

1. right angle
2. acute angle
3. obtuse angle
4. any of the above

Q. Find the values of $x$ and $y$.

1. $x={50}^o,y=6$
2. $x={60}^o,y=4$
3. $x={64}^o,y=9$
4. $x={64}^o,y=4$

Q. A Circle is inscribed in triangle ABC having sides 8 cm, 10 cm, and 12 cm as shown in the given figure. Find AD?

1. 2.5 cm
2. 4 cm
3. 3 cm
4. 5 cm

Q. In $\Delta ABC$, angle $B$ is obtuse. The smallest circle which covers the triangle is the

1. Circle with $AB$ as diameter
2. Circumcircle
3. Circle with $BC$ as diameter
4. Circle with $AC$ as diameter