Let ABC and PQR be two congruent triangles, such that ∠A = ∠P = 90°. If BC = 29 cm, PR = 21 cm, find the value (in cm) of AB.

AB is the diameter of a circle with the center O. P as a point on it. If ∠AOP = 95° then find ∠OBP ?

The measures of two angles of a triangle are in the ratio 3 : 7. If the sum of these two measures is equal to the measure of the third angle, then find the smallest angle.

△ PQR is an equilateral triangle inscribed in a circle. S is any point on the arc QR. Find the measure of ∠PSQ.

In the given figure, 'G' is the centre of the circle. Find the angle ACB when

If m∠C = m∠Z and AC = XZ, then which of the following conditions is necessary for ΔABC and ΔXYZ to be congruent?

In a △ABC, the internal bisectors of ∠B and ∠C meet at O. If ∠BAC = 72°, then the value of ∠BOC is:

If the angles of a triangle are (x - 46)°, (x + 96)° and 8x°, then what is the value of 2x?

In the shown figure, BC is a chord and CD is a tangent through the point C. If ∠AOC = 112°, then find ∠ACD.

In the given figure, \(\Delta\)QPS \(\approx\) \(\Delta\)SRQ. Find the measure of \(\angle\)PSR.

Two circles touch each other externally at P. AB is a direct common tangent to the two circles. If A and B are points of contact and PAB = 65°, then ABP is:

In a circle with center O, PA and PB are the tangents at A and B, respectively, from an external point P. If ∠APB = 24°, then find ∠AOB.

If in ∆ABC and ∆DEF, \(\frac{AB}{DE}=\frac{BC}{FD}\), then they will be similar when:

PQ and PR are tangents to circle, QTR = 55°, find measure of QPR.

A trapezium ABCD is such that all the four points lie on a circle. One of the parallel sides of the trapezium (AB) is the diameter of a circle. If CAB = 40°, find the value of CAD.

In triangle ABC, AD = BD. Also, ∠ADB = 110° and ∠ACD = 53°. Find ∠DAC?

Consider the following statements & choose the correct options:

When two straight lines intersect then,

1. Adjacent angles are supplementary

2. Opposite angles are supplementary

Select the most appropriate option to fill in the blank.
The angles are equal, consequently the sides are _____________.

Select the most appropriate option to fill in the blank.
The angles are equal, consequently the sides are _____________. (Combined Graduate Level Examination Tier I 2022)

Let A = Set of all equilateral triangles

B = Set of all triangles in which one of the medians coincides with the altitude drawn from the vertex

Then, which of the following is true about sets A and B?

What will be the complementary angle of 64°30'?

If ΔBPQ ≅ ΔASR and  ∠A = \(\frac{1}{3}\)∠R = ∠S, then find  ∠Q. (All angles are in degrees).

PQ is a diameter of a circle with centre O. The tangents at R meets PQ produced at A. If ∠RPQ = 27°, then measure of ∠RQP is:

If ΔABC is congruent to ΔDEF, then EF = _________.

O is the centre of a circle, and A is a point on a major arc BC of the circle. ∠BOC and ∠BAC are the angles made by the minor arc BC on the centre and circumference, respectively. If ∠ABO = 40° and ∠ACO = 30°, then find ∠BOC.

In a circle, ABCD is a cyclic quadrilateral in which AE is drawn parallel to CD outside of the circle, and BA is produced to F. If ∠ABC = 85° and ∠FAE = 24°, find the value of ∠BCD.

If O is the ortho centre of ΔABC and ∠BOC = 100°, the measure of ∠BAC is?

In triangle ABC, AP is perpendicular to BC and AQ is the bisector of ∠A. What is the measure of ∠PAQ, if ∠B = 60^o and ∠C = 40^o?

In the given figure, O is the center of the circle. If ∠POQ = 70°, then what is the value of ∠QSR?

In the given figure O is the center of the circle and ∠XPY = 30°. Find the average of the ∠XOY and ∠XZY.

If O is the in-center of a triangle ABC and D be a point on the side BC of triangle ABC, such that OD is perpendicular to BC. If angle BOD = 39^o, then find the value of angle ABC.

In triangle PQR, ∠Q = 78°, PM is perpendicular to QR, RN is perpendicular to PQ, PM and RN intersect at S, and the bisector of ∠SPR and ∠SRP meet at O. Find the value of ∠ROP.

In the given figure CD || AB, ∠CBA = 35°. Find the value of ∠CDB - ∠DBC.

In the given figure AB is tangent with point O on it, ∠DCO = 72° and ∠AOC = 48° then, find the measure of ∠DOB + ∠CEO.

If in the given figure ∠OGL = ∠OCB and ∠LGP = 135°and ∠BOG = 75° then, find ∠OBC.

In the given figure ∠APB = 33°, find the value of \(\sqrt{{1\over3}{{\times∠AOB}}}\).

MN and QR are two chords in a circle with center O and MR is the circle's diameter. When MN and QR are further extended, it meets at a point P outside the Circle. if the ∠RMN = 38°, ∠MPR = 32° then find the angle ∠QNR.

In the given figure CD || AB, ∠CBA = 35°. Find the value of ∠CDB - ∠DBC.

In a circle with centre O,  ABCD is a cyclic quadrilateral with  AB as a diameter of the circle. AD and BC meet at  E. If ∠CED = 66°, then what is the measure of ∠COD?

Points A and B are on a circle with centre O. PAM and PBN are tangents to the circle at A and B, respectively, from a point P outside the circle. Point Q is on the major arc AB such that ∠QAM = 62° and ∠QBN = 50°. Find the measure (in degrees) of ∠APB.

In the following figure, MN is a tangent to a circle with center O at point A. If BC is a diameter and ∠ABC = 42° then find the measure of ∠MAB.

PBA and PDC are two secants. AD is the diameter of the circle with the centre at O. ∠A = 30°, ∠P = 20°. Find the measure of ∠DBC.

In the given figure, O is the center of semicircle, if ∠ AXP=48° , then find ∠ AOB?

In a circle with center O, chords PQ and RS intersect at point T inside the circle. If ∠QTS = 72° and ∠POS = 116°, find ∠QOR.

In the given figure, if PA and PB are tangents to the circle with center O such that ∠APB = 54°, then ∠OBA =?

If ABCD is a square and DEF is an equilateral triangle, then ∠DAE is :

In the given figure two circles touches internally at P . ∠APB = 110° and ∠DPC = 78°, then find ∠APD ?

 In the given figure, AB is the diameter of a circle with center O and AT is a tangent if ∠AOQ = 68°, then what is ∠ATQ?

In the given figure, from the point P two tangents PA and PB are drawn to a circle with centre O and radius 5 cm. From the point O, OC and OD are drawn parallel to PA and PB respectively. If the length of the chord AB is 5 cm, then what is the value (in degrees) of ∠COD?

In ∆ABC, ∠BAC = 60°, and O is a point inside ∆ABC. If ∠OBC is two times ∠OBA and ∠OCB is two times ∠OCA, then what will be the measure of ∠BOC?