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**Q.1. Draw a circle of radius 4 cm. Construct a pair of tangents to it, the angle between which is 60°. Also justify the construction. Measure the distance between the centre of the circle and the point of intersection of tangents.Ans. **Steps of Construction:

Step I: Draw a circle with centre O and radius 4 cm.

Step II: Draw any diameter AOB.

Step III: Draw a radius OC such that ∠BOC = 60°.

Step IV: At C, we draw CM ⊥ OC and at A, we draw AN ⊥ OA.

Step V: Let the two perpendiculars intersect each other at P.

Then, PA and PC are required tangents.

Justification:

Since OA is the radius, so PA has to be a tangent to the circle. Similarly, PC is also tangent to the circle.

Hence, tangents PA and PC are inclined to each other at an angle of 60°.

Ans.

Step I: Draw a line segment BC = 6 cm.

Step II: With centre B and radius 4 cm draw an arc.

Step III: With centre C and radius 9 cm draw another arc which intersects the previous arc at A.

Step IV: Join BA and CA. ABC is the required triangle.

Step V: Through B, draw an acute angle CBX on the side opposite to vertex A.

Step VI: Locate three arcs B

Step VII: Join B

Step VIII: Draw B

Step IX: Draw C'A' || CA intersecting the extended line segment BA at A'.

Thus, ΔA'BC' is the required triangle (ΔA'BC' - ΔABC).

The two triangles are not congruent because, if two triangles are congruent, then they have same shape and size. Here, all tree angles are equal but all three sides are not equal.

Justification:

∵ B

Now,

Again, CC' || AC

ΔABC - ΔA'BC'

∴

Ans.

Ans.

Ans.

In ΔPQR

∠Q = ∠B, PQ = PR = 8 cm.

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