MATHEMATICS Textbook for Class IX>Chapter 10 - Circles>EXERCISE>Q 11

MEDIUM

9th Mizoram Board

IMPORTANT

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$A B C$ and $A D C$ are two right triangles with common hypotenuse $A C$ . Prove that $∠ C A D = ∠ C B D$ .

Important Questions on Circles

MEDIUM

9th Mizoram Board

IMPORTANT

MATHEMATICS Textbook for Class IX>Chapter 10 - Circles>EXERCISE>Q 12

Prove that a cyclic parallelogram is a rectangle.

HARD

9th Mizoram Board

IMPORTANT

MATHEMATICS Textbook for Class IX>Chapter 10 - Circles>EXERCISE (Optional)*>Q 1

Prove that line of centres of two intersecting circles subtends equal angles at the two points of intersection.

HARD

9th Mizoram Board

IMPORTANT

MATHEMATICS Textbook for Class IX>Chapter 10 - Circles>EXERCISE (Optional)*>Q 2

Two chords

A B

and

C D

of lengths

5 c m

and

11 c m

respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between

A B

and

C D

is

6 c m

, find the radius of the circle.

HARD

9th Mizoram Board

IMPORTANT

MATHEMATICS Textbook for Class IX>Chapter 10 - Circles>EXERCISE (Optional)*>Q 3

The lengths of two parallel chords of a circle are $6 cm$ and $8 cm$ . If the smaller chord is at distance $4 cm$ from the centre, what is the distance of the other chord from the centre ?

HARD

9th Mizoram Board

IMPORTANT

MATHEMATICS Textbook for Class IX>Chapter 10 - Circles>EXERCISE (Optional)*>Q 4

Let the vertex of an angle

A B C

be located outside a circle and let the sides of the angle intersect equal chords

A D

and

C E

with the circle. Prove that

∠ A B C

is equal to half the difference of the angles subtended by the chords

A C

and

D E

at the centre.

HARD

9th Mizoram Board

IMPORTANT

MATHEMATICS Textbook for Class IX>Chapter 10 - Circles>EXERCISE (Optional)*>Q 5

Prove that the circle drawn with any side of a rhombus as diameter passes through the point of intersection of its diagonals.

HARD

9th Mizoram Board

IMPORTANT

MATHEMATICS Textbook for Class IX>Chapter 10 - Circles>EXERCISE (Optional)*>Q 6

ABCD

is a parallelogram. The circle through

A, B

and

C

intersect

CD

(produced if necessary) at

E

. Prove that

AE = AD

.

HARD

9th Mizoram Board

IMPORTANT

MATHEMATICS Textbook for Class IX>Chapter 10 - Circles>EXERCISE (Optional)*>Q 7

AC

and

BD

are chords of a circle which bisect each other. Prove that

AC

and

BD

are diameters.