PQR is a triangle such that QP = QR = 15 cm and PR = 18 cm. PN, QM and RT are the altitudes of the triangle which intersect at O.
What is \(QT : QO\) equal to?
4 : 5
Place \(P=(-9,0)\), \(R=(9,0)\); since \(QP=QR=15\), \(Q=(0,12)\) (as \(9^2+12^2=15^2\)). The altitude QM is the y-axis, so \(M=(0,0)\). The foot of the altitude from R onto QP works out to \(T=(-63/25,\,216/25)\), and solving for the intersection of the altitudes gives the orthocentre \(O=(0,27/4)\). Then \(QT=\frac{21}{5}\) and \(QO=12-\frac{27}{4}=\frac{21}{4}\), so \(QT:QO=\frac{21}{5}:\frac{21}{4}=4:5\).
Similar Questions
Each side of a square subtends an angle of 60° at the tip of a tower of height h meters standing at the centre of the square. If l is the length of each side of the square, then what is h 2equal to?
If x is the perimeter, in cm, of the triangle, then which one of the following is correct?
If y is the area in cm² of the triangle, then which one of the following is correct?
What is the ratio of \(AB^2 : BP^2 : PR^2\)?
What is the ratio of the area of Δ PRB to the area of Δ PQC?
What is the ratio of QO to OM?
A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.
Question: ABC is a triangle right-angled at A and AD is perpendicular to BC. If AD = \(7.2\) cm, then what is \(BD \times CD\) equal to?
Statement I: \(AB : AC = 3 : 4\).
Statement II: \(BC = 15\) cm.
Which one of the following is correct in respect of the above Question and Statements?
A square of maximum area is inscribed in an equilateral triangle. If the side of the triangle is equal to \((6+4\sqrt{3})\) cm, then what is the area of the square?
If \(A + B + C = \pi\) \((A, B, C > 0)\) and the angle C is obtuse, then which of the following is/are correct?
I. \(\sin A . \sin B < 1\)
II. \(\tan A . \tan B > 1\)
Select the answer using the code given below:
ABC is a triangle such that \(\angle ABC = 120^\circ\). If BD is the bisector of \(\angle B\) that meets AC at D, then what is the ratio of the area of \(\triangle ABD\) to the area of \(\triangle CBD\)?
Important Questions from Properties of Triangles
In a triangle ABC, a = (1 + √3) cm, b = 2 cm and angle C = 60°, then the other two angles are
Which of the following measures can form a triangle?
If in a triangle ABC, \(\frac{{2\cos A}}{a} + \frac{{\cos B}}{b} + \frac{{2\cos C}}{c} = \frac{a}{{bc}} + \frac{b}{{ca}}\) then the value of the angle A is
In a triangle ABC, sec A (sin B cos C + cos B sin C) equals:
Consider the following statements :
1. ABC is right angled triangle
2. The angles of the triangle are in AP
Which of the statements given above is/are correct ?
