Draw a circle of radius 5 cm . Draw two tangents to this circle so that the angle between the tangents is \( 45^{\circ} \). Draw two radii of the circle so that they make an angle equal to \( 180^{\circ}-45^{\circ}=135^{\circ} \) at the centre of the circle.

To solve this problem, we will follow these steps: 1. **Draw the Circle**: We will draw a circle with a radius of 5 cm. 2. **Draw the Tangents**: We will draw two tangents to the circle such that the angle between them is \( 45^{\circ} \). 3. **Draw the Radii**: We will draw two radii of the circle that make an angle of \( 135^{\circ} \) at the center of the circle. ### Step 1: Draw the Circle - Start by drawing a circle with a center point \( O \) and a radius of 5 cm. ### Step 2: Draw the Tangents - To draw the tangents, we need to find two points on the circle where the tangents will touch. - The angle between the tangents is \( 45^{\circ} \). This means that if we draw a line from the center \( O \) to the point of tangency, the angle between this line and each tangent will be \( 90^{\circ} - \frac{45^{\circ}}{2} = 90^{\circ} - 22.5^{\circ} = 67.5^{\circ} \). - We can place the points of tangency at an angle of \( 22.5^{\circ} \) and \( -22.5^{\circ} \) from a reference line (e.g., the horizontal line through the center). ### Step 3: Draw the Radii - The angle between the two radii at the center \( O \) is \( 135^{\circ} \). - We can draw one radius at \( 0^{\circ} \) (along the horizontal line) and the other radius at \( 135^{\circ} \) from the same reference line. ### Summary of Steps 1. Draw a circle with radius 5 cm centered at point \( O \). 2. Identify points of tangency at angles \( 22.5^{\circ} \) and \( -22.5^{\circ} \) from the horizontal. 3. Draw tangents at these points. 4. Draw one radius at \( 0^{\circ} \) and another at \( 135^{\circ} \). This will give you the desired configuration of the circle, tangents, and radii. If you need a visual representation, please let me know!