Page 49 - ACE YR IGCSE A TOP APPR' TO MATHS

Volume of B : volume of C = 1:8 [6] Angle at the centre of a circle is twice the angle
5 (a) (i) 1 : 2 [1] at the circumference.
(ii) 1 : 4 [2] ∠AEC = 180° – ∠ADC
(iii) 1 : 8 [2] = 180° – 57°
3 = 123°
(b) 100 × = 75 cm 2 [2]
4 Cyclic quadrilaterals [2]
(c) Volume = 7 V [2] (c) ∠OAB = ∠OCB = 90°
8 The angle between the tangent and radius is
always 90°.
Circle theorem ∠OABC = ∠OAB + ∠OCB + ∠AOC + ∠ABC
360° = 90° + 90° + 114° + ∠ABC
1 ∠OTS = 90° ∠ABC = 66°
The angle between a tangent and a radius is 90°. Interior angles of quadrilateral is 360°. [2]
∠ORT = 90° (d) ∠DAE = 90°
The perpendicular from the centre to the chord Angle in semicircle is 90°.
bisects the chord. ∠ADE = 180° – 90° – 54°
∠ROT = 180° – 90° – ∠OTR = 36°
= 90° – (90° – ∠STQ) ∠ADE = ∠ACE
= ∠STQ (shown) [4] ∠ACE = 36°
2 ∠POQ = 2 × ∠PSQ Angles in the same segments are equal.
= 2 × 50° ∠OCA + ∠ACE + ∠ECB = 90°
= 100° The angle between a tangent and a radius is
180° – 100° 90°.
∠QPO =
2 ∠ECB = 90° – 33° – 36°
= 40° = 21° [3]
∠SPO = 180° – 40° – 77° 6 (a) (i) ∠OTP = 180° – 68°
= 63° [3] 2
3 (a) ∠BAD = 90° – ∠DAO = 56°
= 90° – 50° The base angles of an isosceles triangle are
equal.

[2]
= 40°

Penerbitan Pelangi Sdn Bhd. All Rights Reserved. [1]
(b) ∠AOD = 180° – 50° × 2 (ii) ∠TQS = ∠OPT
= 80° = 56°
∠ABC = (180°− 90°− 80°) × 2 Angles in the same segment are equal. [1]
= 20° [2] (iii) ∠QSP + ∠RSQ = ∠SPT
4 (a) ∠RTS = ∠RQS ∠QSP = 56° – 21°
= 180° – 78° – 65° = 35°
= 37° SR // TP, alternate angles are equal. [1]
∠TRS = ∠TQS (iv) ∠PRS = 90°
= 65° Angles in the semicircle is 90°.
∠RST = 180° – 37° – 65° ∠QRP = ∠QSP
= 78° [3] = 35°
(b) ∠RSQ = ∠RTQ Angles in the same segment are equal.
∠RTQ + ∠RTS = 78° + 20° ∠QRS = ∠QRP + ∠PRS
∠RTQ = 98° – 37° = 35° + 90°
= 61° = 125° [2]
∠RSQ = 61° [2] (b) ∠PST = 68°
(c) ∠QRT = 180° – ∠RQS – ∠RSQ – ∠SRT 2
= 180° – 37° – 61° – 65° = 34°
= 17° [2] ∠RST = ∠RSQ + ∠QSP + ∠PST
5 (a) Obtuse ∠AOC = 180° – 33° × 2 = 21° + 35° + 34°
= 114° = 90°
(Isosceles triangle base angles are equal.) RT is the diameter of the circle, thus extension
Reflex ∠AOC = 360° – 114° of TO will pass by R. [2]
= 246° [2]
∠AOC
(b) ∠ADC = Geometric construction
2
114° 1 (a) Correct triangle shape ABC with arc seen
=
2 AB = 12 cm [1]
= 57°

Answers 169

Answers.indd 169 15/03/2022 11:08 AM