class 11

Math

Trigonometry

Solution And Properties Of Triangle

Let $O$be the origin and let PQR be an arbitrary triangle. The point S is such that$OPO˙Q+ORO˙S=ORO˙P+OQO˙S=OQ$.$OR+OPO˙S$Then the triangle PQ has S as its:circumcentre (b) orthocentre (c) incentre (d) centroid

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$x_{2}−c_{2}=y$ then num radius of $Δ$ is (A) $3 y $ (B) $3 c $ (C) $43y $ (D)$43c $

Consider a triangle $ABC$and let $a,bandc$denote the lengths of the sides opposite to vertices $A,B,andC$, respectively. Suppose $a=6,b=10,$and the area of triangle is $153 ˙$If $∠ACB$is obtuse and if $r$denotes the radius of the incircle of the triangle, then the value of $r_{2}$is

Point $P$ is at a height of $25m$ from surface of lake. The angel of elevation from point $P$ on a cloud is $30_{o}$ and angle of depression of image of cloud in water is $60_{o}$ then height of cloud from surface of lake is (A) $75$ (B) $45$ (C) $50$ (D) $49$

In a triangle PQR, P is the largest angle and $cosP=31 $. Further the incircle of the triangle touches the sides PQ, QR and RP at N, L and M respectively, such that the lengths of PN, QL and RM are consecutive even integers. Then possible length(s) of the side(s) of the triangle is (are)

Internal bisector of $∠A$ of triangle ABC meets side BC at D. A line drawn through D perpendicular to AD intersects the side AC at E and the side AB at F. If a, b, c represent sides of $ΔABC$, then

a triangle $ABC$with fixed base $BC$, the vertex $A$moves such that $cosB+cosC=42sin_{2}A ˙$If $a,bandc,$denote the length of the sides of the triangle opposite to the angles $A,B,andC$, respectively, then$b+c=4a$ (b) $b+c=2a$the locus of point $A$is an ellipsethe locus of point $A$is a pair of straight lines

Let $ABCandABC_{′}$be two non-congruent triangles with sides $AB=4,AC=AC_{prime}=22 $and angle $B=30_{0}$. The absolute value of the difference between the areas of these triangles is