  # Important Questions for CBSE Class 10 Maths Chapter 11 - Constructions 2 Mark Question

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CBSE Class 10 Maths Chapter-11 Constructions Important Questions

## 2 Mark Questions

1. In each of the following, give the justification of the construction also:
Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths. Ans. Given: A circle whose centre is O and radius is 6 cm and a point P is 10 cm away from its centre.
To construct: To construct the pair of tangents to the circle and measure their lengths.
Steps of Construction:
(a) Join PO and bisect it. 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 Q and R.
(c) Join PQ and PR.
Then PQ and PR are the required two tangents.
By measurement, PQ = PR = 8 cm
Justification: Join OQ and OR.
Since OQP and ORP are the angles in semicircles.  OQP = ORP
Also, since OQ, OR are radii of the circle, PQ and PR will be the tangents to the circle at Q and R respectively. We may see that the circle with OP as diameter increases the given circle in two points. Therefore, only two tangents can be draw.

2. In figure, PA and PB are tangents from P to the circle with centre O. R is a point on the circle,prove that PC + CR = PD + DR. Ans.
Since length of tangents from an external point to a circle are equal in length  …(i)
And DB = DR
Now PA = PB PC + CA = PD + DB PC + CR = PD + DR [By (i)]

3. The length of tangents from a point A at distance of 26 cm from the centre of the circle is 10cm, what will be the radius of the circle? Ans.
Since tangents to a circle is perpendicular to radius through the point of contact In right , we have    Hence, radius of circle is 24 cm

4. In the given figure, if TP and TQ are the two tangents to a circle with centre O so that , then find  Ans.
Since   5. In the figure, given below PA and PB are tangents to the circle drawn from an external point P. CD is thethird tangent touching the circle at Q. If PB = 10 cm and CQ = 2 cm, what is the length of PC? Ans.
PA=PB=10 cm
CQ = CA = 2 cm
PC = PA – CA = 10 – 2 = 8 cm