HARD
IOQM - PRMO and RMO
IMPORTANT
Earn 100

A conical glass is in the form of a right circular cone. The slant height is 21 and the radius of the top rim of the glass is 14. An ant at the mid-point of a slant line on the outside wall of the glass sees a honey drop diametrically opposite to it on the inside wall of the glass (See the figure.). If d the shortest distance it should crawl to reach the honey drop, what is the integer part of d? (ignore the thickness of the glass.)

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Important Questions on Properties of Triangle

HARD
IOQM - PRMO and RMO
IMPORTANT
EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Properties of Triangle>IOQM - PRMO and RMO 2019 (25-08-2019)>Q 7
In a triangle ABC, it is known that ∠A=100° and AB=AC. The internal angle bisector BD has length 20 units. Find the length of BC to the nearest integer, given that sin10°≈0.174.
HARD
IOQM - PRMO and RMO
IMPORTANT
EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Properties of Triangle>IOQM - PRMO and RMO 2018>Q 8
In a quadrilateral ABCD, it is given that AB=AD=13, BC=CD=20, BD=24. If r is the radius of the circle inscribable in the quadrilateral, then what is the integer closest to r ?
HARD
IOQM - PRMO and RMO
IMPORTANT
EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Properties of Triangle>IOQM - PRMO and RMO 2018>Q 9
In a triangle ABC, the median from B to CA is perpendicular to the median from C to AB. If the median from A to BC is 30, determine BC2+CA2+AB2100.
HARD
IOQM - PRMO and RMO
IMPORTANT
EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Properties of Triangle>IOQM - PRMO and RMO 2018>Q 10
In a triangle ABC, right-angled at A, the altitude through A and the internal bisector of ∠A have lengths 3 units and 4 units, respectively. Find the length of the medium through A.