# Loci and concurrency Questions and answers

Topics

1). The maximum number of tangents which can be drawn from an external point to a circle is
 A). two B). one C). zero D). none of these
2). A circular running track is 10 m wide. The difference in the length of the outer boundary and the inner boundary
I. depends on the length of the track
II. depends on the radius of the inner boundary
III. depends on the area of the track
IV is $$\Large 20 \pi m$$.
Select the correct answer using the codes below:
Codes :

 A). I, II and III B). I and III C). II and III D). IV alone
3). The boundary of the shaded region in the given diagram consists of five semicircular areas. If AB=7cm, BC=3.5cm, CD=7cm and DE=7 cm, then area of the shaded region is

 A). $$\Large \frac{17.5}{2} \times \frac{3.5}{2}\ \pi\ cm^{2}$$ B). $$\Large \frac{17.5 \times 21}{2}\ \pi\ cm^{2}$$ C). $$\Large \frac{35 \times 21}{16}\ \pi\ cm^{2}$$ D). $$\Large \frac{35 \times 21 \pi }{8}\ cm^{2}$$
4). If C is a circle passing through three non-collinear points D,E, F such that DE = EF = DF = 3 cms, then radius of the circle C is
 A). $$\Large \frac{\sqrt{3}}{2}\ cm$$ B). $$\Large \sqrt{3}\ cm$$ C). $$\Large \frac{1}{\sqrt{3}}\ cm$$ D). $$\Large \frac{2}{\sqrt{3}}\ cm$$
5). In a circle of radius 7 cm, an arc subtends an angle of $$\Large 108 ^{\circ}$$ at the centre. The area of the sector is
 A). $$\Large 43.2\ cm^{2}$$ B). $$\Large 44.2\ cm^{2}$$ C). $$\Large 45.2\ cm^{2}$$ D). $$\Large 46.2\ cm^{2}$$

6). Area of the shaded portion in the given figure, where the arcs are quadrants of a circle, is
 A). $$\Large 42\ m^{2}$$ B). $$\Large 56\ m^{2}$$ C). $$\Large 64\ m^{2}$$ D). $$\Large 144\ m^{2}$$
7). In the given figure, PQ is tangent at A; BC is the diameter. If $$\Large \angle ABC = 42 ^{\circ}.\ then\ \angle PAB$$ is equal to
 A). $$\Large 21 ^{\circ}$$ B). $$\Large 42 ^{\circ}$$ C). $$\Large 48 ^{\circ}$$ D). $$\Large 84 ^{\circ}$$
8). If length of the tangent from origin to the circle $$\Large x^{2}+y^{2}-26x+K=0\ is\ 5$$, then K is equal to
 A). $$\Large \sqrt{5}$$ B). 5 C). 10 D). 25
9). If area of the given circle is $$\Large 100 \pi$$ square cm, then side of the square inscribed in the circle is
 A). 10 cm B). $$\Large 10\sqrt{2}\ cm$$ C). 20 cm D). $$\Large 20\sqrt{2}\ cm$$
10). The middle points of all chords (each having the same length) of a circle lie on a
 A). rectangle B). square C). circle D). parallelogram
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