This question was uploaded on 26/08/21 on social media accounts.
The ends of a quarter-circle are 3 and 6 units in length above the baseline and the circle is also touching the baseline. Find the area of the quarter-circle.
Step 1:
Draw a vertical line from the center of the circle to the baseline.
Draw horizontal lines from the end of the quarter circle to the vertical line from the center of the quarter circle.
Give names to all Vertices and intersection of lines.
Let the radius of the quarter-circle be r.
Step 2:
Observe triangles ABN and CAM,
AB = AC = r;
Other angles are similar.
⇒ ⧍ABN ≅ ⧍CAM.
Also,
AO = r,
ON = 3,
⇒ AN = r - 3,
OM = 6,
⇒ AM = r - 6
Step 3:
⧍ABN ≅ ⧍CAM;
⇒ CM = AN = r - 3;
AC = r
Step 4:
⧍CAM is a right-angled triangle.
\[\Rightarrow AM^2+MC^2=AC^2\]
\[\Rightarrow (r-6)^2+(r-3)^2=r^2\]
\[r=3⠀or⠀r=15\]
Clearly r ≠ 3
⇒ r = 15
Area = (²²⁵⁄₄)π
Image Solution:
Puzzle related to Geometry, Circle, Area
