## CBSE Class 10 Maths Chapter-11 Constructions – Free PDF Download

Free PDF download of Important Questions with Answers for CBSE Class 10 Maths Chapter 11 – Constructions prepared by expert Maths teachers from latest edition of CBSE(NCERT) books only by CoolGyan to score more marks in CBSE board examination.

CBSE Class 10 Maths Chapter-11 Constructions Important Questions

**CBSE Class 10 Maths Important Questions Chapter 11 – Constructions**

**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