PA and PB are the tangents drawn to a circle with centre O. If PA= 6 cm and  APB = 600 , then find the length of the chord AB.

[Class 10] PA and PB are the tangents drawn to a circle with centre O - CBSE Class 10 Sample Paper for 2022 Boards - Maths Basic [Term 2]

part 2 - Question 9 - CBSE Class 10 Sample Paper for 2022 Boards - Maths Basic [Term 2] - Solutions of Sample Papers for Class 10 Boards - Class 10
part 3 - Question 9 - CBSE Class 10 Sample Paper for 2022 Boards - Maths Basic [Term 2] - Solutions of Sample Papers for Class 10 Boards - Class 10

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PA and PB are the tangents drawn to a circle with centre O. If PA= 6 cm and  APB = 600 , then find the length of the chord AB. We know that Tangent from external point are equal ∴ PA = PB Since angles opposite equal sides are equal Thus, ∠ PAB = ∠ PBA By Angle Sum property in Δ APB ∠ APB + ∠ PAB + ∠ PBA = 180° 60° + ∠ PAB + ∠ PAB = 180° 60° + 2∠ PAB = 180° 2∠ PAB = 180° − 60° 2∠ PAB = 120° ∠ PAB = (120° )/2 ∠ PAB = 60° Thus, in Δ APB ∠ PAB = ∠ PBA = 60° And, ∠ APB = 60° Since all angles are 60°, ∴ Δ APB is an equilateral triangle 60° + ∠ PAB + ∠ PAB = 180° 60° + 2∠ PAB = 180° 2∠ PAB = 180° − 60° 2∠ PAB = 120° ∠ PAB = (120° )/2 ∠ PAB = 60° Thus, in Δ APB ∠ PAB = ∠ PBA = 60° And, ∠ APB = 60° Since all angles are 60°, ∴ Δ APB is an equilateral triangle Since in equilateral triangle All sides are equal ∴ AB = AP = 6 cm

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo