(6)Two circles, each of radius 7 cms, intersect
each other. The distance between their centres
is 72 cms. Find the area common to both the
circles.
(7)PQR is an equilateral triangle with side
18 cms. A circle is drawn on segment QR as
diameter. Find the length of the arc of this circle
intercepted within the triangle.
Answers
Answer:
28 cm²
9π cm
Step-by-step explanation:
Two circles, each of radius 7 cm,
intersect each other. The distance
between their centres is 7√2cm. Find
the area common to both the circles.
As both radius are 7 and distance between centers = 7√2
=> Angle between Radius = 90° (as 7² + 7² = (7√2)²)
Hence its a square formed by center points & intersection points
Area of Square = 7*7 = 49 cm²
Angle at center by Arc = 90°
Area of Both Arcs = 2 * (90/360) π 7²
= 2 (1/4) (22/7) * 7²
= 77 cm²
the area common to both the circles. = 77 - 49 = 28 cm²
PQR is an equilateral triangle with side
18 cms. A circle is drawn on segment QR as
diameter. Find the length of the arc of this circle
intercepted within the triangle.
As circle id drawn on QR = 18 cm
=> Radius = 9 cm
semicircle wiill exist inside triangle
=> Length of arc = πR = 9π cm