Q1.Answer the following questions
1) How many parts a circle can divide a plane into?
2) Which is the longest chord of the circle?
3) In the given figure, O is the center of the circle with chords AP and BP being produced to
R and Q respectively. If ∠QPR = 35°, find the measure of ∠AOB.
4) Three angles of a quadrilateral are equal and the fourth angle is equal to 144°. Find each
of the equal angles of the quadrilateral
5) In the given figure, what is the measure of angle x?
6) A side of equilateral triangle is 6cm. Find its area
Answers
Answer:
(1)A circle divides the plane into three parts:
(2)chord that passes through the center of a circle is called a diameter and is the longest chord.
(3)
∠APB = ∠RPQ = 35°
Now, ∠AOB and ∠APB are angles subtended by an arc AB at centre and at the remaining part of the circle .
∴∠AOB = 2∠APB = 2 × 35° = 70°
(4)Let each equal angle of given quadrilateral be x.
We know that, sum of all interior angles of a quadrilateral is 360°.
∴ x + x + x + 144° = 360°
3x = 360° - 144°
3x = 216°
x = 72°
Hence each equal angle of the quadrilateral is of 72° measures.
(5)
EFD+∠FED=x (Exterior angle property of a triangle)
⇒28
o
+42
o
=∠x
⇒∠x=70
(6)
Step-by-step explanation:
a=6cm, b=6cm, c=6cm
∴s=
2
a+b+c
=
2
6+6+6
=9cm
∴ Area of the equilateral triangle
=
s(s−a)(s−b)(s−c)
=
9(9−6)(9−6)(9−6)
=
9(3)(3)(3)
=9
3
cm
2
1) How many parts a circle can divide a plane into?
ans.three parts
A circle divides the plane into three parts: The points INSIDE the circle.
2) Which is the longest chord of the circle?
ans.diameter
A chord that passes through the center of a circle is called a diameter and is the longest chord.
3) In the given figure, O is the center of the circle with chords AP and BP being produced to
ans. ∠APBand∠QPR will be equal as they are vertically opposite angles. Also, we know angle made by a chord at point on the circle is half of the angle made at the center of the circle.
4) Three angles of a quadrilateral are equal and the fourth angle is equal to 144°. Find each
ans.Three angles of a quadrilateral are equal and the fourth angle is equal to 144°. Find each of the equal angles of the quadrilateral .
5) In the given figure, what is the measure of angle x?
ans. ∠EFD+∠FED=x (Exterior angle property of a triangle)
⇒28
o
+42
o
=∠x
⇒∠x=70
o
6) A side of equilateral triangle is 6cm. Find its area
ans.a=6cm, b=6cm, c=6cm
∴s=
2
a+b+c
=
2
6+6+6
=9cm
∴ Area of the equilateral triangle
=
s(s−a)(s−b)(s−c)
=
9(9−6)(9−6)(9−6)
=
9(3)(3)(3)
=9
3
cm
2