Question

draw a circle of radius 3 cm take two point P and Q on one of its extended diameter each at a distance of 7 cm from its centre draw tangents to the circle from these two point P and Q​

Answer 1

Answer:

1. Draw a circle of radius 3cm .

2. from point O extand the diameter each at a distance of 7cm from its center.

3. Draw perpendicular bisecter of PO and OQ.

4. Name the point M¹ and M² which bisect the line PO and OQ.

5. take M¹ and M² as center and draw circles.

6. These two circles draw four arcs on first circle.

7. Name them as A,B,C,D .

8. Join A and D to p and B and C to Q.

These are required tangents.

Answer 2

Answer:

Steps of Construction:

(a) Bisect PO. Let M be the mid-point of PO.

(b) Taking M as centre and MO as radius, draw a circle. Let it intersects the given circle at the points A and B.

(c) Join PA and PB. Then PA and PB are the required two tangents.

(d) Bisect QO. Let N be the mid-point of QO.(e) Taking N as centre and NO as radius, draw a circle. Let it intersects the given circle at the points C and D.

(f) Join QC and QD.

Then QC and QD are the required two tangents.

Justification:

Join OA and OB.

Then PAO is an angle in the semicircle and therefore ∠PAO = 90° .

PA ⊥ OA

Since OA is a radius of the given circle, PA has to be a tangent to the circle. Similarly, PB is also a tangent to the circle.

Again join OC and OD.

Then ∠QCO is an angle in the semicircle and therefore ∠QCO = 90° .

Since OC is a radius of the given circle, QC has to be a tangent to the circle. Similarly, QD is also a tangent to the circle.

Step-by-step explanation:

Hope this helps you ✌️