Quantum CAT Also Useful for XAT>Chapter 12 - SNAP>CMAT>Q 130

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IMPORTANT

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In the following figure the four equispaced vertices of a regular dodecagon are connected in such a way that they create a quadrilateral, as shown below. If each side of the quadrilateral is $\sqrt{3} + 1 cm$ , find the circumradius of the dodecagon.

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Important Questions on Geometry

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IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 12 - SNAP>CMAT>Q 131

A regular dodecagon is inscribed in a circle of radius

1 cm

. Find the area of the dodecagon

HARD

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 12 - SNAP>CMAT>Q 132

Circle with radii

3, 4

and

5

touch each other externally, if

P

is the point of intersection of tangents to these circles at their points of contact. Find the distance of

P

from the point of contact.

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CAT

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Quantum CAT Also Useful for XAT>Chapter 12 - SNAP>CMAT>Q 133

Three points

X, Y

and

Z

are concyclic to the larger circle with radius

15 cm

and there is another concentric circle with radius

8 cm

such that

XY

and

XZ

are tangents to the smaller circle. At how many points does

YZ

intersect the larger circle?

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CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 12 - SNAP>CMAT>Q 136

Triangle

ABC

inscribes a circle with centre

O

and inradius

\sqrt{6} cm

. The inradius

OD

divides side

BC

at

D

, such that

BD = 2 cm

and

DC = 8 cm

. Find the ratio

AB : AC

.

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CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 12 - SNAP>CMAT>Q 137

A circle with radius

12 cm

has two perpendicular chords

AB

and

CD

intersecting at a point

R

, other than the centre

O

, where

RD = 6 cm

and

RB = 18 cm

. Find the length of

AR

.

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CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 12 - SNAP>CMAT>Q 138

There are two tangents

AT

and

BT

on a circle of radius

30 cm

. A line

OT (= 50 cm)

connects the centre

O

with the external point

T

. Another tangent

CD

touches the circle at

P

such that

C

and

D

lie on the line segments

AT

and

BT

, respectively. Points

P

and

T

lie on the same side of the circle. Find the maximum possible area (in sq.

cm

) of the circle inscribed in the triangle

CDT

.

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IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 12 - SNAP>CMAT>Q 139

In the following figure there are two smaller circles inscribed in a larger circle touching each other. The centres of all the three circles fall on $AB$ , and $CD$ is tangent to both the interior circles. If $CD = 16 cm$ , find the area of the shaded region.

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Quantum CAT Also Useful for XAT>Chapter 12 - SNAP>CMAT>Q 140

In the following figure $AB = 21 cm, BC = 15 cm, AC = 24 cm .$ Point $P$ is the mid-point of arc $AC$ , and the chord $BD$ Bisects chord $AC$ at $P$ . Find the ratio $BP / PD$ .