Question

12. Draw a circle of radius 4 cm. Take two points P and Q on one of its extended diameter each at a 3

distance of 6 cm from its centre. Draw tangents to the circle from these two points P and Q.​

Answer 1

Step-by-step explanation:

draw the circle with given radius and extend the diameter by 3 CM then draw perpendicular bisectors by taking more than half distance using compass and draw a circle touching the two intersection points of perpendicular bisectors and now we see that both the circles touch each other at two points draw 2 separate lines touching those points from extended point.These are tangents of the given circle

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 ✌️