Geometry - Study Mode

[#61] PQRS is a cyclic quadrilateral in which PQ = 14.4 cm, QR = 12.8 cm and SR = 9.6 cm. If PR bisects QS, what is the length of PS?
Correct Answer

(D) 19.2 cm

[#62] In the given figure, chords PQ and RS intersect each other at point L. Find the length of RL.
Correct Answer

(D) 6 cm

Explanation

Solution: RL × LS = PL × LQ 6 × RL= 9 × 4 RL = 6 cm

[#63] Let D and E be two points on the side BC of ΔABC such that AD = AE and ∠BAD = ∠EAC. If AB = (3x + 1) cm, BD = 9 cm, AC = 34 cm and EC = (y + 1) cm, then the value of (x + y) is:
Correct Answer

(A) 19

Explanation

Solution: ΔABC Isosceles Δ 3x + 1 = 34 x = 11 From Pythagoras Triplet AP = 30 cm PC = BP = 16 cm DP = 7 cm PC = 7 + y + 1 16 = 8 + y y = 8 x + y = 11 + 8 = 19

[#64] In the given figure, PQRS is a square inscribed in a circle of radius 4 cm. PQ is produced till point Y. From Y a tangent is drawn to the circle at point R. What is the length (in cm) of SY?
Correct Answer

(A) $$4sqrt {10} $$

Explanation

Solution: ∠PRQ = 45° ∠ORY = 90° ∠QRY = 45° RQ = QY Diagonal = 8 = Diameter Side $$ = frac{8}{{sqrt 2 }} = 4sqrt 2 $$ In ΔSPY, SY 2 = SP 2 + PY 2 = 128 + 32 = 160 SY = $$4sqrt {10} $$

[#65] ABC is an isosceles triangle where AB = AC which is circumscribed about a circle. If P is the point where the circle touches the side BC, then which of the following is true?
Correct Answer

(A) BP = PC

Explanation

Solution: Here given that = AB = AC AQ + BQ = AR + RC We know that BQ = PB & PC = RC AQ + PB = AR + PC Also AQ = AR AR + PB = AR + PC PB = PC