Question

for a given circle with centre O and radius OA, if two arcs B and C are drawn on the circumference of the circle from 1 by taking the measurement of OA as the radius of the arc. what will be the shape of the triangle formed by joining the point 1 , B and C ?

Answer 1

Answer:

Radius, r = 4, and center (h, k) = (-2, 3).

We know that the equation of a circle with centre (h, k) and radius r is given as

→ (x – h)² + (y – k)² = r² \: \: \: ….(1)→(x–h)²+(y–k)²=r²….(1)

Now, substitute the radius and center values in (1), we get

Therefore, the equation of the circle is

→ (x + 2)²+ (y – 3)² = (4)²→(x+2)²+(y–3)²=(4)²

→ x²+ 4x + 4 + y² – 6y + 9 = 16→x²+4x+4+y²–6y+9=16

Now, simplify the above equation, we get:

→ x² + y²+ 4x – 6y – 3 = 0→x²+y²+4x–6y–3=0

Thus, the equation of a circle with center (-2, 3) and radius 4 is :

→ x² + y²+ 4x – 6y – 3 = 0→x²+y²+4x–6y–3=0

Answer 2

The shape of the triangle formed will be right angle triangle.

Given:

Circle with center O and radius OA, if two arcs B and C are drawn on the circumference of the circle from 1 by taking the measurement of OA as the radius of the arc.

To Find:

The shape of the triangle formed by joining the point 1 , B and C

Solution:

∵ We know angle subtended by an arc at centre is double the angle subtended at any point or circumference.

⇒ Angle subtended by arc AB at O= Double the angle subtended at C

⇒∠AOB=2∠ACB

∵AOB is a straight line.

⇒∠AOB= 180°

⇒2∠ACB= 180°

⇒∠ACB= 90°

∴ Angle subtended by arc AB or semi circle is 90° and it is a right angle triangle.

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