Question

Draw a circle of radius 5cm. from a point 8 cm away from its center, construct a pair of tangents to the circle. Find the length of tangents.

Answer 1

Hint: With the help of a compass, draw a circle of radius 5 cm. Keep a measuring scale with you to measure the line at the end of the answer. We will take the help of a perpendicular bisector while making the diagram.

Complete Step-by-step answer:

Step 1: Draw a circle of the radius given in the question. Here the radius is 5 cm so we will make a circle of radius 5 cm.

Step 2: Mark a point C 8cm away from the center of the circle i.e. B.

Step 3: Draw a perpendicular bisector of the line BC.

Step 4: The point where the perpendicular bisector intersects the line BC, take that point and make another circle. Remember to make the perpendicular bisector right so that it won’t make your measurements wrong at the end of the answer.

Step 5: Now, make a line starting from point C to the point where the recently drawn circle touches the circle with center B. Mark those points as P or Q.

Step 6: measure the lines PC and PQ with a measuring scale and the length of the tangents drawn 8cm away from a circle of radius 4cm is 6cm.

Hence, the length of the tangent PC and PQ is 6cm.

Note: Whenever making the circle, always make sure that the radius is right. While drawing a second circle, try to make dotted lines that it won’t look too congested. When you make tangents, make sure that the compass has the right adjustments.