# CBSE [Delhi]_X_Mathematics_2015_Set III

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• Q1

In Fig. 1, PA and PB are tangents to the circle with centre O such that ∠APB=50o.  Write the measure of∠OAB.

Marks:1

Join OC.

• Q2

Marks:1

• Q3

The tops of two towers of height x and y, standing on level ground, subtend angles of 30° and 60° respectively at the centre of the line joining their feet, then find x:y.

Marks:1

• Q4

A letter of English alphabet is chosen at random. Determine the probability that the chosen letter is a constant.

Marks:1

Number of English alphabet = 26
Number of constants = 21

Probability of choosing a constant = 21/26

• Q5

From a point T outside a circle of centre O, tangents TP and TQ are drawn to the circle. Prove that OT is the right bisector of line segment PQ.

Marks:2

Given: TP and TQ are tangents to circle and OT intersects chord PQ at R.

To Prove: OT bisects PQ at right angle.

• Q6

Find the middle term of the A.P.
6, 13, 20, …, 216.

Marks:2

• Q7

In Fig. 2, AB is the diameter of a circle with centre O and AT is a tangent. If  .

Marks:2

• Q8

If A(5, 2), B(2,–2) and C(–2, t) are the vertices of a right angled triangle with angle B = 90°, then find the value of t.

Marks:2

In right angled triangle, ABC,

By Pythagoras Theorem,

AC2 = AB2 + BC2

(5 + 2)2 +(2 – t)2 =(5 – 2)2 +(2 +2)2 +(2 + 2)2
+(–2 – t)2

72 + 4 – 4t + t2 = 9 + 16 + 16 + 4 + 4t + t2
53 – 4t = 45 + 4t
53 – 45 = 8t
t = 8/8 = 1

• Q9

Marks:2