HARD

IOQM - PRMO and RMO

IMPORTANT

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Let $A B C$ be a triangle such that $A B = A C$ . Suppose the tangent to the circumcircle of $A B C$ at $B$ is perpendicular to $A C$ . Find $∠ A B C$ measured in degrees.

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Important Questions on Triangle

HARD

IOQM - PRMO and RMO

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Triangle>IOQM - PRMO and RMO 2019 (25-08-2019)>Q 11

The centre of the circle passing through the midpoints of the sides of an isosceles triangle

A B C

lies on the circumcircle of triangle

A B C

. If the larger angle of triangle

A B C

α °

and the smaller one is

β °

, then what is the value of

α - β

MEDIUM

IOQM - PRMO and RMO

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Triangle>IOQM - PRMO and RMO 2019 (25-08-2019)>Q 12

A friction-less board has the shape of an equilateral triangle of side length

1

meter with bouncing walls along the sides. A tiny super bouncy ball is fired from vertex

A

towards the side

B C .

The ball bounces off the walls of the board nine times before it hits a vertex for the first time. The bounces are such that the angle of incidence equals the angle of reflection. The distance travelled by the ball in meters is of the form

\sqrt{N},

where

N

is an integer. What is the value of

N ?

HARD

IOQM - PRMO and RMO

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Triangle>IOQM - PRMO and RMO 2019 (25-08-2019)>Q 13

Let

A B C

be an acute angled triangle with

A B = 15

and

B C = 8 .

Let

D

be a point on

A B

such that

B D = B C .

Consider points

E

A C

such that

∠ D E B = ∠ B E C .

α

denotes the product of all possible values of

A E,

find

\frac{[α]}{10}

, where

[α]

is the integer part of

α .

HARD

IOQM - PRMO and RMO

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Triangle>IOQM - PRMO and RMO 2018>Q 14

Let

A B

be a chord of a circle with centre

O .

Let

C

be a point on the circle such that

∠ A B C = 30 °

and

O

lies inside the triangle

A B C

. Let

D

be a point on

A B

such that

∠ D C O = ∠ O C B = 20 ° .

Find the measure of

∠ C D O

in degrees.

HARD

IOQM - PRMO and RMO

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Triangle>IOQM - PRMO and RMO 2018>Q 15

Triangles

A B C

and

D E F

are such that

∠ A = ∠ D, A B = D E = 17, B C = E F = 10

and

A C - D F = 12

. What is

A C + D F

HARD

IOQM - PRMO and RMO

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Triangle>IOQM - PRMO and RMO 2018>Q 16

Let

A B C

be an acute-angled triangle and let

H

be its orthocentre. Let

G_{1}, G_{2}

and

G_{3}

be the centroids of the triangles

H B C, H C A

and

H A B,

respectively. If the area of triangle

G_{1} G_{2} G_{3}

7

units, what is the area of triangle

A B C

HARD

IOQM - PRMO and RMO

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 12 - Triangle>IOQM - PRMO and RMO 2018>Q 17

Let

D

be an interior point of the side

B C

of a triangle

A B C .

Let

I_{1}

and

I_{2}

be the incentres of triangles

A B D

and

A C D

, respectively. Let

A I_{1}

and

A I_{2}

meet

B C

E

and

F

, respectively. If

∠ B I_{1} E = 60 °,

what is the measure of

∠ C l_{2} F

in degrees?

Let ABC be a triangle such that AB=AC. Suppose the tangent to the circumcircle of ABC at B is perpendicular to AC. Find ∠ABC measured in degrees.

Important Questions on Triangle

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Let $A B C$ be a triangle such that $A B = A C$ . Suppose the tangent to the circumcircle of $A B C$ at $B$ is perpendicular to $A C$ . Find $∠ A B C$ measured in degrees.