Question

Construct a square PQRS PQ = 6.5cm, QR=4.5cm Draw a circle to touch round PQR find the radius of the circle​

Answer 1

Constructing a square PQRS (PQ = 6.5 cm) and inscribing a circle within it, the radius of the circle is approximately 5.75 cm, touching sides at P, Q, R, and S.

To construct a square PQRS with PQ = 6.5 cm and inscribe a circle within the square, we follow these steps. Draw a square ABCD with sides PQ = QR = RS = SP = 6.5 cm. Now, inscribe a circle within the square, touching all four sides at points P, Q, R, and S. The center of the circle, O, is also the intersection point of the diagonals AC and BD of the square. This circle is known as the incircle.

To find the radius of the incircle, we use the fact that the radius is perpendicular to the sides of the square at the point of tangency. Thus, the radius is a bisector of the right angle formed by the sides. The radius can be calculated using the Pythagorean theorem by considering the right-angled triangle formed by the radius, half of PQ, and half of QR.

`\[ r^2 = \left((6.5)/(2)\right)^2 + \left((6.5)/(2)\right)^2 \]`

`\[ r^2 = 16.5625 + 16.5625 \]`

`\[ r^2 = 33.125 \]`

`\[ r = √(33.125) \]`

r = 5.75

Therefore, the radius of the inscribed circle is approximately 5.75 cm.

The question probable may be:

Construct a square PQRS PQ = 6.5cm Draw a circle to touch round PQR find the radius of the circle​