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.
CBSE Class 10 Sample Paper for 2022 Boards - Maths Basic [Term 2]
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CBSE Class 10 Sample Paper for 2022 Boards - Maths Basic [Term 2]
Last updated at April 16, 2024 by Teachoo
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