Theorem 2: Perpendicular from the Center to a Chord Bisects the Chord

Q.

In the given figure, lengths of the chords $AB$ and $CD$ are $12cm$ and $18cm$ respectively and distance between them is $15cm$. Find the radius of the circle.

1. None of these

2. $\sqrt{119}cm$

3. $\sqrt{113}cm$

4. $\sqrt{117}cm$

Q.

In the given figure, radius of the circle is $5cm$ and perpendicular distance from the centre of the circle to the chord, $AC$ is $3cm$.

Find the length of the chord, $AC$.

1. $4cm$

2. $5cm$

3. $7cm$

4. $8cm$

Q.

Two circles of radii $4cm$ and $3cm$ intersect at two points and the distance between their centres is $5cm$. Find the length of the common chord.

1. $4.8cm$

2. $2.8cm$

3. $7cm$

4. $5.5cm$

Q.

Find the area of trapezium (in ${cm}^2$).

1. 45
2. 48
3. 49

4. 40

Q.

The length of the common chord of two intersecting circles is 30 cm. If the diameters of these two circles are 50 cm & 34 cm, the distance between their centers is ____ cm.

1. 30

2. 24
3. 32
4. 28

Q.

S1: $AM=\frac{AP}{2},BN=\frac{BP}{2}$

S2: $O{O}^{\prime }=AM+BN$

Choose the correct option.

1. Only S1 is true.

2. Only S2 is true.

3. Both statements are true.

4. S1 is true & S2 is false.

Q.

The perpendicular to a chord from the centre of the circle divides the chord in ratio of

1. 1:1

2. 1:4

3. 1:2

4. 1:3

Q.

An equilateral triangle $ABC,$ whose side is $6cm,$ is inscribed in a circle. Find the radius of the circle.

1. 2√2 cm

2. 2√3 cm

3. 3√3 cm

4. 3 cm

Q.

Two circles of radii $5cm$ and $6cm$ with common centre are drawn. There is a line $AB$ such that it is chord to both the circles. $CD=8cm.$ Find the distance of the chord from centre and the length of $AC$ respectively.

1. 2, 2.35

2. 2.35, 2

3. 3, 2

4. 2.16, 2.35

Q.

What is the relation between AM & MB in the given figure?

1. AM = MB

2. AM = 2MB

3. 2AM = MB

4. 3AM = 2MB