In a triangle PQR, let `anglePQR = 30^(@)` and the sides PQ and QR have lengths `10 sqrt3` and 10, respectively. Then, which of the following statement(s) is (are) TRUE ?

In a DeltaPQR, Let /_PQR=30^(@) and the sides PQ and QR have lengths 10sqrt3 and 10, respectively. Then, which of the following statement(s) is (are) TRUE (a) /_QPR=45^(@) (b) The area of the DeltaPQR is 25sqrt3 and /_QRP=120^(@) (c) The radius of the incircle of the DeltaPQR" is "10sqrt3-15 (d) The area of the circumcircle of the DeltaPQR" is"100 pi

Consider a triangle PQR having sides of lengths p,q,r opposite to the angles P,Q,R respectively. Then which of the following statements is (are) true?

PQR is a triangle right-angled at Q. If X and Y are the mid-points of the sides PQ and QR respectively, then which one of the following is not correct?

In two triangles PQR and LMN, PQ = QR, angleP=angleMandQR=LN , then which of the following is true?

In triangle PQR, squareQ=90^o , squareR=x^o . Lengths of the sides PQ , QR and PR are a,b,c respectively. Which among the following is tanx^0 (a/c,b/a,a/b,b/c) .

Let PQR be a triangle . Let veca=overline(QR),vecb = overline(RP) and vecc= overline(PQ).if |veca|=12, |vecb|=4sqrt3and vecb.vecc= 24 then which of the following is (are) true ?

Let PQR be a triangle . Let veca=overline(QR),vecb = overline(RP) and vecc= overline(PQ).if |veca|=12, |vecb|=4sqrt3and vecb.vecc= 24 then which of the following is (are) true ?

In a triangle PQR ,P is the largest angle and cos P = 1/3 . further the triangle toches the side 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)

In a triangle PQR, PQ=QR, A and B are the mid-points of bar(QR) and bar(PR) respectively. A circle passes through P,Q, A and B. Then which of the following is necessarily true?